Finite Group Databasebeta

← C7×#26191 #13203407

Subgroups — C7×#26191 #13203407

Order 1792.

766 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3096C211yesmaximal, characteristic, complemented
2C7×#3045C211yesmaximal, characteristic
3C7×#2952C211yesmaximal, characteristic, complemented
4C7×#2912C211yesmaximal, characteristic, complemented
5C7×#2094C211yesmaximal, characteristic, complemented
6C7×#2090C211yesmaximal, characteristic, complemented
7C7×#2079C211yesmaximal, characteristic, complemented
8C7×#2037C211yesmaximal, characteristic, complemented
9C7×#1931C211yesmaximal, characteristic, complemented
10C7×#1922C211yesmaximal, characteristic, complemented
11C7×#1907C211yesmaximal, characteristic, complemented
12C7×#1883C211yesmaximal, characteristic, complemented
13C7×#1876C211yesmaximal, characteristic, complemented
14C7×#1859C211yesmaximal, characteristic, complemented
15C7×#1859C211yesmaximal, characteristic, complemented
16C2×C7×AGL(1,ℤ/8)C2211yescharacteristic
17C2×C7×#135C2211yescharacteristic
18C2×C7×#131C2211yescharacteristic
19C7×#535C2211yescharacteristic
20C7×#520C2211yescharacteristic
21C7×#520C2211yescharacteristic
22C7×#520C2211yescharacteristic
23C7×#482—21no—
24C7×#482—21no—
25C7×#481—21no—
26C7×#480—21no—
27C7×#464—21no—
28C7×#463—21no—
29C7×#460—21no—
30C7×#459—21no—
31C7×#442—21no—
32C7×#441—21no—
33C4×C7×SD16—21no—
34C4×C7×SD16—21no—
35C7×#428—21no—
36C7×#428—21no—
37C7×#428C2211yescharacteristic
38C7×#428C2211yescharacteristic
39C7×#428C2211yescharacteristic
40C7×#427—21no—
41C7×#427C2211yescharacteristic
42C2×C7×#106—21no—
43C2×C7×#106C2211yescharacteristic
44C2×C7×#106C2211yescharacteristic
45C7×#424C2211yescharacteristic
46C2×C7×#104C2211yescharacteristic
47C2×C7×#104C2211yescharacteristic
48C7×#418C2211yescharacteristic
49C7×#417C2211yescharacteristic
50C7×#417C2211yescharacteristic
51C7×#417C2211yescharacteristic
52C2×C7×#102C2211yescharacteristic
53C2×C7×#102C2211yescharacteristic
54C2×C7×#100C2211yescharacteristic
55C7×#408C2211yescharacteristic
56C7×#405C2211yescharacteristic
57C7×#390C2211yescharacteristic
58C7×#384C2211yescharacteristic
59C7×#343C2211yescharacteristic
60C7×#343C2211yescharacteristic
61C7×#343C2211yescharacteristic
62C7×#341C2211yescharacteristic
63C7×#341C2211yescharacteristic
64C7×#339C2211yescharacteristic
65C7×#339C2211yescharacteristic
66C7×#336C2211yescharacteristic
67#26191C711yesmaximal, characteristic, direct product factor, Sylow
68C2×C7×#41C2311yescharacteristic
69C2×C7×#41C2311yescharacteristic
70C22×C7×D4C2311yescharacteristic
71C7×AGL(1,ℤ/8)—22no—
72C7×AGL(1,ℤ/8)—22no—
73C7×#135—22no—
74C7×#135—22no—
75C2×C7×Q16D411yescharacteristic
76C2×C7×SD16—21no—
77C2×C7×SD16D411yescharacteristic
78C2×C7×SD16D411yescharacteristic
79C2×C7×D8—21no—
80C2×C7×D8D411yescharacteristic
81C7×#131—22no—
82C7×#131—22no—
83C2×C7×M16—21no—
84C2×C7×M16C2311yescharacteristic
85C2×C7×M16C2311yescharacteristic
86C2×C7×M16C2311yescharacteristic
87C2×C7×M16C2311yescharacteristic
88C22×C7×C8—21no—
89C22×C7×C8C2311yescharacteristic
90C22×C7×C8C2311yescharacteristic
91C7×#127—21no—
92C7×#124—21no—
93C7×#121—21no—
94C7×#121—21no—
95C7×#120—41no—
96C4×C7×Q8—21no—
97C4×C7×Q8—21no—
98C4×C7×Q8—21no—
99C4×C7×D4—21no—
100C4×C7×D4—21no—
101C4×C7×D4—21no—
102C4×C7×D4—41no—
103C4×C7×D4—41no—
104C4×C7×D4—41no—
105C7×#117—21no—
106C7×#117—21no—
107C7×#117—21no—
108C7×#117C2311yescharacteristic
109C7×#117C2311yescharacteristic
110C2×C7×C4⋊C4—21no—
111C2×C7×C4⋊C4—21no—
112C2×C7×C4⋊C4—21no—
113C2×C7×C4⋊C4—41no—
114C2×C7×C4⋊C4C2311yescharacteristic
115C2×C7×C4⋊C4C2311yescharacteristic
116C2×C7×C4⋊C4C2311yescharacteristic
117C2×C7×C22⋊C4—41no—
118C2×C42×C7C2311yescharacteristic
119C7×#107—21no—
120C7×#107—21no—
121C7×#107—21no—
122C7×#107D411yescharacteristic
123C7×#107D411yescharacteristic
124C7×#106—21no—
125C7×#106—21no—
126C7×#106—21no—
127C7×#106—21no—
128C7×#106—21no—
129C7×#106—21no—
130C7×#106—21no—
131C7×#106D411yescharacteristic
132C7×#106D411yescharacteristic
133C7×C4⋊C8—21no—
134C7×C4⋊C8—21no—
135C7×#104—22no—
136C7×#104—22no—
137C7×#103—21no—
138C7×#103—21no—
139C7×#103—21no—
140C7×#102—21no—
141C7×#102—21no—
142C7×#102—21no—
143C7×#102—21no—
144C7×#102—21no—
145C7×#102—21no—
146C7×#102—21no—
147C7×#102—21no—
148C7×#102—21no—
149C7×#100—22no—
150C7×C22⋊C8—21no—
151C7×C22⋊C8—21no—
152C7×#97—21no—
153C4×C7×C8—21no—
154#3096C2×C711yescharacteristic, complemented
155#3045C2×C711yescharacteristic
156#2952C2×C711yescharacteristic, complemented
157#2912C2×C711yescharacteristic, complemented
158#2094C2×C711yescharacteristic, complemented
159#2090C2×C711yescharacteristic, complemented
160#2079C2×C711yescharacteristic, complemented
161#2037C2×C711yescharacteristic, complemented
162#1931C2×C711yescharacteristic, complemented
163#1922C2×C711yescharacteristic, complemented
164#1907C2×C711yescharacteristic, complemented
165#1883C2×C711yescharacteristic, complemented
166#1876C2×C711yescharacteristic, complemented
167#1859C2×C711yescharacteristic, complemented
168#1859C2×C711yescharacteristic, complemented
169C24×C7—21no—
170C7×#41—21no—
171C7×#41—21no—
172C7×#41—21no—
173C7×#41—21no—
174C7×#41—21no—
175C7×#41—21no—
176C7×#41#4112yes—
177C7×#41#4112yes—
178C2×C7×Q8C2×D411yescharacteristic
179C2×C7×Q8C2×D411yescharacteristic
180C2×C7×D4—21no—
181C2×C7×D4—21no—
182C2×C7×D4—21no—
183C2×C7×D4—21no—
184C2×C7×D4—21no—
185C2×C7×D4—21no—
186C2×C7×D4—21no—
187C2×C7×D4—21no—
188C2×C7×D4—41no—
189C2×C7×D4—41no—
190C2×C7×D4C2×D411yescharacteristic
191C2×C7×D4C2×D411yescharacteristic
192C22×C4×C7—21no—
193C22×C4×C7—21no—
194C22×C4×C7—21no—
195C22×C4×C7—21no—
196C22×C4×C7—21no—
197C22×C4×C7—21no—
198C22×C4×C7—41no—
199C22×C4×C7—41no—
200C22×C4×C7—41no—
201C22×C4×C7C2411yescharacteristic
202C7×Q16—22no—
203C7×SD16—22no—
204C7×SD16—22no—
205C7×SD16—42no—
206C7×D8—22no—
207C7×D8—42no—
208C7×M16—24no—
209C7×M16—21no—
210C7×M16—21no—
211C7×M16—21no—
212C7×M16—21no—
213C7×M16—21no—
214C7×M16—21no—
215C7×M16—21no—
216C7×M16#4112yes—
217C2×C7×C8—24no—
218C2×C7×C8—21no—
219C2×C7×C8—21no—
220C2×C7×C8—21no—
221C2×C7×C8—21no—
222C2×C7×C8—21no—
223C2×C7×C8—21no—
224C2×C7×C8—21no—
225C2×C7×C8—21no—
226C2×C7×C8C2×D411yescharacteristic
227C2×C7×C8C2×D411yescharacteristic
228C2×C7×C8C2×D411yescharacteristic
229C2×C7×C8C2×D411yescharacteristic
230C7×C4⋊C4—21no—
231C7×C4⋊C4—21no—
232C7×C4⋊C4—21no—
233C7×C4⋊C4—21no—
234C7×C4⋊C4—21no—
235C7×C4⋊C4—21no—
236C7×C4⋊C4—41no—
237C7×C4⋊C4—41no—
238C7×C4⋊C4—41no—
239C7×C4⋊C4—82no—
240C7×C4⋊C4C2×D411yescharacteristic
241C7×C4⋊C4C2×D411yescharacteristic
242C7×C4⋊C4C2×D411yescharacteristic
243C7×C4⋊C4C2×D411yescharacteristic
244C7×C22⋊C4—21no—
245C7×C22⋊C4—21no—
246C7×C22⋊C4—41no—
247C7×C22⋊C4—41no—
248C7×C22⋊C4—41no—
249C7×C22⋊C4—41no—
250C7×C22⋊C4—41no—
251C7×C22⋊C4—82no—
252C42×C7—21no—
253C42×C7—21no—
254C42×C7—21no—
255C42×C7—21no—
256C42×C7—41no—
257C42×C7—41no—
258C42×C7—41no—
259C2×AGL(1,ℤ/8)C22×C711yescharacteristic
260C2×#135C22×C711yescharacteristic
261C2×#131C22×C711yescharacteristic
262#535C22×C711yescharacteristic
263#520C22×C711yescharacteristic
264#520C22×C711yescharacteristic
265#520C22×C711yescharacteristic
266#482—21no—
267#482—21no—
268#481—21no—
269#480—21no—
270#464—21no—
271#463—21no—
272#460—21no—
273#459—21no—
274#442—21no—
275#441—21no—
276C4×SD16—21no—
277C4×SD16—21no—
278#428—21no—
279#428—21no—
280#428C22×C711yescharacteristic
281#428C22×C711yescharacteristic
282#428C22×C711yescharacteristic
283#427—21no—
284#427C22×C711yescharacteristic
285C2×#106—21no—
286C2×#106C22×C711yescharacteristic
287C2×#106C22×C711yescharacteristic
288#424C22×C711yescharacteristic
289C2×#104C22×C711yescharacteristic
290C2×#104C22×C711yescharacteristic
291#418C22×C711yescharacteristic
292#417C22×C711yescharacteristic
293#417C22×C711yescharacteristic
294#417C22×C711yescharacteristic
295C2×#102C22×C711yescharacteristic
296C2×#102C22×C711yescharacteristic
297C2×#100C22×C711yescharacteristic
298#408C22×C711yescharacteristic
299#405C22×C711yescharacteristic
300#390C22×C711yescharacteristic
301#384C22×C711yescharacteristic
302#343C22×C711yescharacteristic
303#343C22×C711yescharacteristic
304#343C22×C711yescharacteristic
305#341C22×C711yescharacteristic
306#341C22×C711yescharacteristic
307#339C22×C711yescharacteristic
308#339C22×C711yescharacteristic
309#336C22×C711yescharacteristic
310C23×C7—21no—
311C23×C7—21no—
312C23×C7—41no—
313C23×C7—41no—
314C23×C7—41no—
315C23×C7—81no—
316C23×C7—81no—
317C23×C7H(5,𝔽2)11yescharacteristic
318C7×Q8—21no—
319C7×Q8—21no—
320C7×Q8—21no—
321C7×Q8#12312yes—
322C7×D4—22no—
323C7×D4—22no—
324C7×D4—21no—
325C7×D4—21no—
326C7×D4—21no—
327C7×D4—41no—
328C7×D4—41no—
329C7×D4—41no—
330C7×D4—41no—
331C7×D4—41no—
332C7×D4—41no—
333C7×D4—161no—
334C7×D4—161no—
335C7×D4#12312yes—
336C2×C4×C7—21no—
337C2×C4×C7—22no—
338C2×C4×C7—22no—
339C2×C4×C7—22no—
340C2×C4×C7—21no—
341C2×C4×C7—21no—
342C2×C4×C7—21no—
343C2×C4×C7—21no—
344C2×C4×C7—21no—
345C2×C4×C7—41no—
346C2×C4×C7—41no—
347C2×C4×C7—41no—
348C2×C4×C7—41no—
349C2×C4×C7—41no—
350C2×C4×C7—41no—
351C2×C4×C7—41no—
352C2×C4×C7—81no—
353C2×C4×C7—81no—
354C2×C4×C7—81no—
355C2×C4×C7—161no—
356C2×C4×C7—161no—
357C2×C4×C7—161no—
358C2×C4×C7C22×D411yescharacteristic
359C2×C4×C7C22×D411yescharacteristic
360C2×C4×C7C2×#4111yescharacteristic
361C2×C4×C7C2×#4111yescharacteristic
362C2×C4×C7C2×#4111yescharacteristic
363C2×C4×C72−1+411yescharacteristic
364C7×C8—21no—
365C7×C8—21no—
366C7×C8—21no—
367C7×C8—22no—
368C7×C8—21no—
369C7×C8—41no—
370C7×C8—41no—
371C7×C8—41no—
372C2×#41C23×C711yescharacteristic
373C2×#41C23×C711yescharacteristic
374C22×D4C23×C711yescharacteristic
375AGL(1,ℤ/8)—22no—
376AGL(1,ℤ/8)—22no—
377#135—22no—
378#135—22no—
379C2×Q16C7×D411yescharacteristic
380C2×SD16—21no—
381C2×SD16C7×D411yescharacteristic
382C2×SD16C7×D411yescharacteristic
383C2×D8—21no—
384C2×D8C7×D411yescharacteristic
385#131—22no—
386#131—22no—
387C2×M16—21no—
388C2×M16C23×C711yescharacteristic
389C2×M16C23×C711yescharacteristic
390C2×M16C23×C711yescharacteristic
391C2×M16C23×C711yescharacteristic
392C22×C8—21no—
393C22×C8C23×C711yescharacteristic
394C22×C8C23×C711yescharacteristic
395#127—21no—
396#124—21no—
397#121—21no—
398#121—21no—
399#120—41no—
400C4×Q8—21no—
401C4×Q8—21no—
402C4×Q8—21no—
403C4×D4—21no—
404C4×D4—21no—
405C4×D4—21no—
406C4×D4—41no—
407C4×D4—41no—
408C4×D4—41no—
409#117—21no—
410#117—21no—
411#117—21no—
412#117C23×C711yescharacteristic
413#117C23×C711yescharacteristic
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—41no—
418C2×C4⋊C4C23×C711yescharacteristic
419C2×C4⋊C4C23×C711yescharacteristic
420C2×C4⋊C4C23×C711yescharacteristic
421C2×C22⋊C4—41no—
422C2×C42C23×C711yescharacteristic
423#107—21no—
424#107—21no—
425#107—21no—
426#107C7×D411yescharacteristic
427#107C7×D411yescharacteristic
428#106—21no—
429#106—21no—
430#106—21no—
431#106—21no—
432#106—21no—
433#106—21no—
434#106—21no—
435#106C7×D411yescharacteristic
436#106C7×D411yescharacteristic
437C4⋊C8—21no—
438C4⋊C8—21no—
439#104—22no—
440#104—22no—
441#103—21no—
442#103—21no—
443#103—21no—
444#102—21no—
445#102—21no—
446#102—21no—
447#102—21no—
448#102—21no—
449#102—21no—
450#102—21no—
451#102—21no—
452#102—21no—
453#100—22no—
454C22⋊C8—21no—
455C22⋊C8—21no—
456#97—21no—
457C4×C8—21no—
458C22×C7—21no—
459C22×C7—21no—
460C22×C7—22no—
461C22×C7—41no—
462C22×C7—41no—
463C22×C7—41no—
464C22×C7—41no—
465C22×C7—41no—
466C22×C7—82no—
467C22×C7—81no—
468C22×C7—81no—
469C22×C7—81no—
470C22×C7—161no—
471C22×C7#53911yescharacteristic
472C22×C7D4211yescharacteristic
473C22×C7#55311yescharacteristic
474C4×C7—22no—
475C4×C7—42no—
476C4×C7—41no—
477C4×C7—41no—
478C4×C7—41no—
479C4×C7—41no—
480C4×C7—41no—
481C4×C7—81no—
482C4×C7—81no—
483C4×C7—81no—
484C4×C7C2×#12311yescharacteristic
485C4×C7#52511yescharacteristic
486C4×C7#54711yescharacteristic
487C4×C7#54811yescharacteristic
488C24—21no—
489#41—21no—
490#41—21no—
491#41—21no—
492#41—21no—
493#41—21no—
494#41—21no—
495#41C7×#4112yes—
496#41C7×#4112yes—
497C2×Q8C2×C7×D411yescharacteristic
498C2×Q8C2×C7×D411yescharacteristic
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—41no—
508C2×D4—41no—
509C2×D4C2×C7×D411yescharacteristic
510C2×D4C2×C7×D411yescharacteristic
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4C24×C711yescharacteristic
521Q16—22no—
522SD16—22no—
523SD16—22no—
524SD16—42no—
525D8—22no—
526D8—42no—
527M16—24no—
528M16—21no—
529M16—21no—
530M16—21no—
531M16—21no—
532M16—21no—
533M16—21no—
534M16—21no—
535M16C7×#4112yes—
536C2×C8—24no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8C2×C7×D411yescharacteristic
546C2×C8C2×C7×D411yescharacteristic
547C2×C8C2×C7×D411yescharacteristic
548C2×C8C2×C7×D411yescharacteristic
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—41no—
556C4⋊C4—41no—
557C4⋊C4—41no—
558C4⋊C4—82no—
559C4⋊C4C2×C7×D411yescharacteristic
560C4⋊C4C2×C7×D411yescharacteristic
561C4⋊C4C2×C7×D411yescharacteristic
562C4⋊C4C2×C7×D411yescharacteristic
563C22⋊C4—21no—
564C22⋊C4—21no—
565C22⋊C4—41no—
566C22⋊C4—41no—
567C22⋊C4—41no—
568C22⋊C4—41no—
569C22⋊C4—41no—
570C22⋊C4—82no—
571C42—21no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—41no—
576C42—41no—
577C42—41no—
578C2×C7—21no—
579C2×C7—21no—
580C2×C7—42no—
581C2×C7—81no—
582C2×C7—161no—
583C2×C7#244311yescharacteristic
584C2×C7#328811yescharacteristic
585C2×C7#329111yescharacteristic
586C23—21no—
587C23—21no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—81no—
592C23—81no—
593C23C7×H(5,𝔽2)11yescharacteristic
594Q8—21no—
595Q8—21no—
596Q8—21no—
597Q8C7×#12312yes—
598D4—22no—
599D4—22no—
600D4—21no—
601D4—21no—
602D4—21no—
603D4—41no—
604D4—41no—
605D4—41no—
606D4—41no—
607D4—41no—
608D4—41no—
609D4—161no—
610D4—161no—
611D4C7×#12312yes—
612C2×C4—21no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—81no—
629C2×C4—81no—
630C2×C4—81no—
631C2×C4—161no—
632C2×C4—161no—
633C2×C4—161no—
634C2×C4C22×C7×D411yescharacteristic
635C2×C4C22×C7×D411yescharacteristic
636C2×C4C2×C7×#4111yescharacteristic
637C2×C4C2×C7×#4111yescharacteristic
638C2×C4C2×C7×#4111yescharacteristic
639C2×C4C7×2−1+411yescharacteristic
640C8—21no—
641C8—21no—
642C8—21no—
643C8—22no—
644C8—21no—
645C8—41no—
646C8—41no—
647C8—41no—
648C7#2619111yescharacteristic, direct product factor, Sylow
649C22—21no—
650C22—21no—
651C22—22no—
652C22—41no—
653C22—41no—
654C22—41no—
655C22—41no—
656C22—41no—
657C22—82no—
658C22—81no—
659C22—81no—
660C22—81no—
661C22—161no—
662C22C7×#53911yescharacteristic
663C22C7×D4211yescharacteristic
664C22C7×#55311yescharacteristic
665C4—22no—
666C4—42no—
667C4—41no—
668C4—41no—
669C4—41no—
670C4—41no—
671C4—41no—
672C4—81no—
673C4—81no—
674C4—81no—
675C4C2×C7×#12311yescharacteristic
676C4C7×#52511yescharacteristic
677C4C7×#54711yescharacteristic
678C4C7×#54811yescharacteristic
679C2—21no—
680C2—21no—
681C2—42no—
682C2—81no—
683C2—161no—
684C2C7×#244311yescharacteristic
685C2C7×#328811yescharacteristic
686C2C7×#329111yescharacteristic
subgroupG/H
center, socleC22×C7D42
commutator, Frattini, cosocleC22×C4C24×C7
prime radicalC7×#3045C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C7 ◁ C22×C4×C7 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C7×#3096C2semidirect
3. C7×#2952C2semidirect
4. C7×#2912C2semidirect
5. C7×#2094C2semidirect
6. C7×#2090C2semidirect
7. C7×#2079C2semidirect
8. C7×#2037C2semidirect
9. C7×#1931C2semidirect
10. C7×#1922C2semidirect
11. C7×#1907C2semidirect
12. C7×#1883C2semidirect
13. C7×#1876C2semidirect
14. C7×#1859C2semidirect
15. C7×#1859C2semidirect
67. #26191C7direct (N × H)
154. #3096C2×C7semidirect
156. #2952C2×C7semidirect
157. #2912C2×C7semidirect
158. #2094C2×C7semidirect
159. #2090C2×C7semidirect
160. #2079C2×C7semidirect
161. #2037C2×C7semidirect
162. #1931C2×C7semidirect
163. #1922C2×C7semidirect
164. #1907C2×C7semidirect
165. #1883C2×C7semidirect
166. #1876C2×C7semidirect
167. #1859C2×C7semidirect
168. #1859C2×C7semidirect
648. C7#26191direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C7×#30962
C7×#30452
C7×#29522
C7×#29122
C7×#20942
C7×#20902
C7×#20792
C7×#20372
C7×#19312
C7×#19222
C7×#19072
C7×#18832
C7×#18762
C7×#18592
#261917