Finite Group Databasebeta

← #13360466

Subgroups — #13360466

Order 1792.

1010 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2323C211yesmaximal, characteristic, complemented
2C2×#89821C211yesmaximal, characteristic
3C2×C4×#1143C211yesmaximal, characteristic, complemented
4#11739681C211yesmaximal, characteristic
5C2×#89769C211yesmaximal, characteristic, complemented
6#11729450C211yesmaximal, characteristic, complemented
7#11729385C211yesmaximal, characteristic, complemented
8#11727433C211yesmaximal, characteristic, complemented
9#11727428C211yesmaximal, characteristic, complemented
10#11727374C211yesmaximal, characteristic, complemented
11#11727369C211yesmaximal, characteristic, complemented
12#11727269C211yesmaximal, characteristic
13#11727267C211yesmaximal, characteristic, complemented
14C4×#6381C211yesmaximal, characteristic, complemented
15#11727228C211yesmaximal, characteristic, complemented
16C2×C7×C22⋊Q8C2211yescharacteristic
17C2×C4×C7×Q8C2211yescharacteristic
18C2×C7×#117C2211yescharacteristic
19C22×#1143C2211yescharacteristic
20C2×#6493C2211yescharacteristic
21C22×#1136C2211yescharacteristic
22C23×C7⋊C8C2211yescharacteristic
23C2×C4×D28C2211yescharacteristic
24C7×#391C2211yescharacteristic
25C7×#389—21no—
26C7×#389C2211yescharacteristic
27C7×#388—21no—
28C7×#388—21no—
29C7×#387—21no—
30C7×#380C2211yescharacteristic
31C4×C7×C4⋊C4C2211yescharacteristic
32C2×#6409C2211yescharacteristic
33C2×#6409C2211yescharacteristic
34C2×#6409C2211yescharacteristic
35#89984C2211yescharacteristic
36#89821C418yescomplemented
37C4×#1143—24no—
38#89769—24no—
39#89762—21no—
40#89761—21no—
41C2×#6383C2211yescharacteristic
42C2×#6383C2211yescharacteristic
43C2×#6383C2211yescharacteristic
44C2×#6382C2211yescharacteristic
45C2×#6381C2211yescharacteristic
46C2×#6381C2211yescharacteristic
47#89729—21no—
48#89728—21no—
49#89711C2211yescharacteristic
50C4×C4⋊Dic7C2211yescharacteristic
51#89700C2211yescharacteristic
52C2×#6377C2211yescharacteristic
53C2×#6377C2211yescharacteristic
54C2×C4×C7⋊C8C2211yescharacteristic
55C2×C4×C7⋊C8C2211yescharacteristic
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#89324C2211yescharacteristic
60#89324C2211yescharacteristic
61#89324C2211yescharacteristic
62#21535—71nomaximal, Sylow
63C22×C7×Q8C2311yescharacteristic
64C23×C4×C7C2311yescharacteristic
65C22×C22⋊D7—21no—
66C22×D28C2311yescharacteristic
67C22×C4×D7—21no—
68C7×C22⋊Q8—22no—
69C7×C22⋊Q8C2×C414yescomplemented
70C4×C7×Q8—22no—
71C4×C7×Q8—22no—
72C7×#117—22no—
73C7×#117—22no—
74C2×C7×C4⋊C4—21no—
75C2×C7×C4⋊C4—21no—
76C2×C7×C4⋊C4—21no—
77C2×C7×C4⋊C4D411yescharacteristic
78C2×C7×C4⋊C4D411yescharacteristic
79C2×C7×C4⋊C4C2311yescharacteristic
80C2×C7×C4⋊C4C2311yescharacteristic
81C2×C7×C4⋊C4C2311yescharacteristic
82C2×C7×C22⋊C4—21no—
83C2×C7×C22⋊C4—21no—
84C2×C7×C22⋊C4D411yescharacteristic
85C2×C7×C22⋊C4D411yescharacteristic
86C2×C42×C7—21no—
87C2×C42×C7—21no—
88C2×C42×C7C2311yescharacteristic
89C2×C42×C7C2311yescharacteristic
90C2×C22⋊Dic7—21no—
91C2×#1143—22no—
92C2×#1143—22no—
93C2×#1143C2×C414yes—
94#6493—22no—
95#6493C2×C414yes—
96C2×(C2×D7)⋊C4—21no—
97C2×(C2×D7)⋊C4—21no—
98C2×(C2×D7)⋊C4—21no—
99C2×(C2×D7)⋊C4—21no—
100C2×C4⋊Dic7C2311yescharacteristic
101C2×C4⋊Dic7C2311yescharacteristic
102C2×C4⋊Dic7C2311yescharacteristic
103C2×Dic7⋊C4—21no—
104C2×C4×Dic7—21no—
105C2×#1136—22no—
106C2×#1136—22no—
107C2×#1136C2×C414yescomplemented
108C22×C7⋊C8—22no—
109C22×C7⋊C8—22no—
110C22×C7⋊C8—22no—
111C22×C7⋊C8C2311yescharacteristic
112C22×C7⋊C8C2311yescharacteristic
113C22×C7⋊C8C2311yescharacteristic
114C22×C7⋊C8C2311yescharacteristic
115C4×D28—22no—
116C4×D28—22no—
117C7×#95—21no—
118C7×#95—21no—
119C7×#95—21no—
120C7×#95—21no—
121C7×#95—21no—
122#6409—22no—
123#6409—22no—
124#6409C2×C414yescomplemented
125C7⋊#95—21no—
126C7⋊#95—21no—
127C7⋊#95—21no—
128#6383—22no—
129#6383—22no—
130#6383C2×C414yes—
131#6382—22no—
132#6381—22no—
133#6381C2×C414yescomplemented
134#6377—22no—
135#6377—22no—
136C4×C7⋊C8—22no—
137C4×C7⋊C8D414yescomplemented
138C2×#468—71no—
139C2×C4×SD16—71no—
140C2×#405—71no—
141#2324—71no—
142#2323D711yescharacteristic, complemented
143#1973—71no—
144#1943—71no—
145#1934—71no—
146#1933—71no—
147#1893—71no—
148#1892—71no—
149#1809—71no—
150C4×#107—71no—
151#1763—71no—
152#1762—71no—
153C24×C7C2×D411yescharacteristic
154C23×D7—21no—
155C2×C7×Q8—21no—
156C2×C7×Q8—21no—
157C2×C7×Q8—21no—
158C2×C7×Q8—21no—
159C2×C7×Q8—21no—
160C2×C7×Q8C22×C412yes—
161C22×C4×C7—21no—
162C22×C4×C7—21no—
163C22×C4×C7—21no—
164C22×C4×C7—21no—
165C22×C4×C7—21no—
166C22×C4×C7—21no—
167C22×C4×C7—21no—
168C22×C4×C7—21no—
169C22×C4×C7C22×C412yes—
170C22×C4×C7C2×D411yescharacteristic
171C22×C4×C7C2×D411yescharacteristic
172C22×C4×C7C2×D411yescharacteristic
173C22×C4×C7C2×D411yescharacteristic
174C22×C4×C7C2×D411yescharacteristic
175C22×C4×C7#4112yes—
176C22×C4×C7C2411yescharacteristic
177C2×C22⋊D7—24no—
178C2×C22⋊D7—81no—
179C2×C22⋊D7—81no—
180C22×Dic7—21no—
181C22×Dic7—21no—
182C22×Dic7—21no—
183C2×D28—21no—
184C2×D28—21no—
185C2×D28—21no—
186C2×D28—21no—
187C2×D28—21no—
188C2×D28C22×C412yes—
189C2×C4×D7—42no—
190C2×C4×D7—81no—
191C2×C4×D7—81no—
192C7×C4⋊C4—24no—
193C7×C4⋊C4—22no—
194C7×C4⋊C4—22no—
195C7×C4⋊C4—21no—
196C7×C4⋊C4—21no—
197C7×C4⋊C4—21no—
198C7×C4⋊C4—21no—
199C7×C4⋊C4—21no—
200C7×C4⋊C4—42no—
201C7×C4⋊C4—81no—
202C7×C4⋊C4C22×C412yes—
203C7×C22⋊C4—24no—
204C7×C22⋊C4—22no—
205C7×C22⋊C4—22no—
206C7×C22⋊C4—81no—
207C42×C7—21no—
208C42×C7—21no—
209C42×C7—42no—
210C42×C7—81no—
211C42×C7C2×D412yes—
212C42×C7#4112yes—
213C22⋊Dic7—81no—
214#1143—28no—
215(C2×D7)⋊C4—24no—
216(C2×D7)⋊C4—42no—
217(C2×D7)⋊C4—81no—
218(C2×D7)⋊C4—81no—
219C4⋊Dic7—21no—
220C4⋊Dic7—21no—
221C4⋊Dic7—21no—
222C4⋊Dic7—21no—
223C4⋊Dic7—21no—
224C4⋊Dic7C22×C412yes—
225Dic7⋊C4—81no—
226C4×Dic7—81no—
227#1136—28no—
228C2×C7⋊C8—28no—
229C2×C7⋊C8—21no—
230C2×C7⋊C8—21no—
231C2×C7⋊C8—21no—
232C2×C7⋊C8—21no—
233C2×C7⋊C8—21no—
234C2×C7⋊C8—21no—
235C2×C7⋊C8C22×C412yes—
236C2×C7⋊C8C22×C412yes—
237C2×C7⋊C8C2×D412yes—
238C2×C7⋊C8C2×D412yes—
239C2×C7⋊C8#4112yes—
240C2×C7⋊C8#4112yes—
241C22×SD16—71no—
242C22×M16—71no—
243C23×C8—71no—
244C2×C22⋊Q8C2×D711yescharacteristic
245C2×#121—71no—
246C2×C4×Q8C2×D711yescharacteristic
247C2×C4×D4—71no—
248C2×#117C2×D711yescharacteristic
249#468—78no—
250C4×SD16—144no—
251C2×#107—71no—
252C2×#107—71no—
253C2×#106—71no—
254C2×#103—71no—
255C2×#103—71no—
256C2×#103—71no—
257C2×#102—71no—
258C2×#102—71no—
259C2×#102—71no—
260#405—144no—
261C2×#97—71no—
262C2×#97—71no—
263C2×C4×C8—71no—
264C2×C4×C8—71no—
265#391C2×D711yescharacteristic
266#390—71no—
267#390—141no—
268#389—21no—
269#389—71no—
270#389C2×D711yescharacteristic
271#388—21no—
272#388—21no—
273#388—141no—
274#387—21no—
275#386—141no—
276#385—141no—
277#380—71no—
278#380C2×D711yescharacteristic
279C4×C4⋊C4—71no—
280C4×C4⋊C4C2×D711yescharacteristic
281#340—71no—
282#340—71no—
283#340—71no—
284#340—71no—
285#340—71no—
286#340—71no—
287C23×C7—21no—
288C23×C7—21no—
289C23×C7—21no—
290C23×C7—21no—
291C23×C7—21no—
292C23×C7—21no—
293C23×C7C4×D412yes—
294C23×C7C22×D411yescharacteristic
295C22×D7—22no—
296C22×D7—41no—
297C22×D7—41no—
298C22×D7—41no—
299C22×D7—41no—
300C22×D7—41no—
301C22×D7—41no—
302C7×Q8—22no—
303C7×Q8—22no—
304C7×Q8—41no—
305C7×Q8—41no—
306C2×C4×C7—21no—
307C2×C4×C7—21no—
308C2×C4×C7—21no—
309C2×C4×C7—21no—
310C2×C4×C7—21no—
311C2×C4×C7—21no—
312C2×C4×C7—22no—
313C2×C4×C7—22no—
314C2×C4×C7—22no—
315C2×C4×C7—22no—
316C2×C4×C7—22no—
317C2×C4×C7—22no—
318C2×C4×C7—21no—
319C2×C4×C7—21no—
320C2×C4×C7—21no—
321C2×C4×C7—21no—
322C2×C4×C7—21no—
323C2×C4×C7—21no—
324C2×C4×C7—41no—
325C2×C4×C7—41no—
326C2×C4×C7—41no—
327C2×C4×C7—41no—
328C2×C4×C7—41no—
329C2×C4×C7—41no—
330C2×C4×C7—41no—
331C2×C4×C7—41no—
332C2×C4×C7—41no—
333C2×C4×C7—41no—
334C2×C4×C7C4×D412yes—
335C2×C4×C7#12112yes—
336C2×C4×C7#12112yes—
337C2×C4×C7C23×C411yescharacteristic
338C2×C4×C7C22×D411yescharacteristic
339C2×C4×C7C2×#4111yescharacteristic
340C2×C4×C7C2×#4111yescharacteristic
341C2×C4×C7C2×#4111yescharacteristic
342C2×C4×C7C2×#4111yescharacteristic
343C22⋊D7—84no—
344C2×Dic7—22no—
345C2×Dic7—41no—
346C2×Dic7—41no—
347C2×Dic7—41no—
348C2×Dic7—41no—
349C2×Dic7—41no—
350C2×Dic7—41no—
351C2×Dic7—41no—
352C2×Dic7—41no—
353D28—22no—
354D28—22no—
355D28—41no—
356D28—41no—
357C4×D7—84no—
358C7⋊C8—22no—
359C7⋊C8—22no—
360C7⋊C8—22no—
361C7⋊C8C4×D414yes—
362C22×Q8C22×D711yescharacteristic
363C22×D4—71no—
364C22×D4—141no—
365C23×C4—141no—
366C23×C4C22×D711yescharacteristic
367C2×SD16—74no—
368C2×SD16—142no—
369C2×SD16—142no—
370C2×M16—74no—
371C2×M16—142no—
372C2×M16—142no—
373C22×C8—71no—
374C22×C8—71no—
375C22×C8—71no—
376C22×C8—71no—
377C22×C8—142no—
378C22×C8—142no—
379C22×C8—142no—
380C22⋊Q8—22no—
381C22⋊Q8C4×D714yescomplemented
382#121—74no—
383#121—142no—
384C4×Q8—22no—
385C4×Q8—22no—
386C4×D4—142no—
387C4×D4—142no—
388#117—22no—
389#117—22no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—71no—
394C2×C4⋊C4—71no—
395C2×C4⋊C4—71no—
396C2×C4⋊C4—141no—
397C2×C4⋊C4C22⋊D711yescharacteristic
398C2×C4⋊C4C22⋊D711yescharacteristic
399C2×C4⋊C4C22×D711yescharacteristic
400C2×C4⋊C4C22×D711yescharacteristic
401C2×C4⋊C4C22×D711yescharacteristic
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—141no—
405C2×C22⋊C4—141no—
406C2×C22⋊C4—141no—
407C2×C22⋊C4—141no—
408C2×C22⋊C4—141no—
409C2×C22⋊C4C22⋊D711yescharacteristic
410C2×C22⋊C4C22⋊D711yescharacteristic
411C2×C42—21no—
412C2×C42—21no—
413C2×C42—141no—
414C2×C42C22×D711yescharacteristic
415C2×C42C22×D711yescharacteristic
416#107—74no—
417#107—142no—
418#106—142no—
419#103—74no—
420#103—142no—
421#103—142no—
422#102—74no—
423#102—142no—
424#102—142no—
425#97—142no—
426#97—142no—
427C4×C8—74no—
428C4×C8—142no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—141no—
435#95—141no—
436#95—141no—
437C22×C7—22no—
438C22×C7—22no—
439C22×C7—22no—
440C22×C7—41no—
441C22×C7—41no—
442C22×C7—41no—
443C22×C7—41no—
444C22×C7C2×C4×D411yescharacteristic
445C22×C7C2×#12111yescharacteristic
446C22×C7#53211yescharacteristic
447C22×C7#57611yescharacteristic
448C22×C7#57711yescharacteristic
449C22×C7#57711yescharacteristic
450C22×C7#57811yescharacteristic
451C2×D7—42no—
452C2×D7—42no—
453C2×D7—42no—
454C2×D7—81no—
455C2×D7—81no—
456C2×D7—81no—
457C2×D7—81no—
458C4×C7—22no—
459C4×C7—22no—
460C4×C7—22no—
461C4×C7—42no—
462C4×C7—41no—
463C4×C7—41no—
464C4×C7—42no—
465C4×C7—81no—
466C4×C7—81no—
467C4×C7C2×C4×D411yescharacteristic
468C4×C7C4×#4111yescharacteristic
469C4×C7#52511yescharacteristic
470C4×C7#52911yescharacteristic
471Dic7—42no—
472Dic7—81no—
473Dic7—81no—
474C24—141no—
475C24C2×C22⋊D711yescharacteristic
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8C2×C4×D712yes—
482C2×D4—72no—
483C2×D4—144no—
484C2×D4—141no—
485C2×D4—141no—
486C2×D4—141no—
487C2×D4—141no—
488C2×D4—141no—
489C2×D4—561no—
490C2×D4—561no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—141no—
500C22×C4—141no—
501C22×C4—141no—
502C22×C4—282no—
503C22×C4—561no—
504C22×C4—561no—
505C22×C4C2×C4×D712yes—
506C22×C4#115712yes—
507C22×C4C2×C22⋊D711yescharacteristic
508C22×C4C2×C22⋊D711yescharacteristic
509C22×C4C2×C22⋊D711yescharacteristic
510C22×C4C2×C22⋊D711yescharacteristic
511C22×C4C2×C22⋊D711yescharacteristic
512C22×C4C23×D711yescharacteristic
513SD16—148no—
514M16—148no—
515C2×C8—72no—
516C2×C8—72no—
517C2×C8—72no—
518C2×C8—72no—
519C2×C8—72no—
520C2×C8—72no—
521C2×C8—148no—
522C2×C8—141no—
523C2×C8—141no—
524C2×C8—141no—
525C2×C8—141no—
526C2×C8—141no—
527C2×C8—141no—
528C4⋊C4—24no—
529C4⋊C4—22no—
530C4⋊C4—22no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—42no—
537C4⋊C4—72no—
538C4⋊C4—81no—
539C4⋊C4—141no—
540C4⋊C4—141no—
541C4⋊C4—141no—
542C4⋊C4—141no—
543C4⋊C4—141no—
544C4⋊C4—561no—
545C4⋊C4C2×C4×D712yes—
546C22⋊C4—24no—
547C22⋊C4—22no—
548C22⋊C4—22no—
549C22⋊C4—81no—
550C22⋊C4—144no—
551C22⋊C4—282no—
552C22⋊C4—561no—
553C22⋊C4—561no—
554C22⋊C4—561no—
555C42—21no—
556C42—21no—
557C42—42no—
558C42—81no—
559C42—561no—
560C42D4×D712yes—
561C42#115912yes—
562C2×C7—42no—
563C2×C7C4×#12111yescharacteristic
564C2×C7#294611yescharacteristic
565C2×C7#294711yescharacteristic
566C2×C7#305711yescharacteristic
567C2×C7#306111yescharacteristic
568C2×C7#317811yescharacteristic
569C2×C7#317911yescharacteristic
570D7—82no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—142no—
578C23—281no—
579C23—281no—
580C23—281no—
581C23—281no—
582C23—281no—
583C23—281no—
584C23C4×C22⋊D712yes—
585C23C22×C22⋊D711yescharacteristic
586Q8—22no—
587Q8—22no—
588Q8—41no—
589Q8—41no—
590D4—142no—
591D4—142no—
592D4—281no—
593D4—281no—
594D4—564no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—142no—
624C2×C4—281no—
625C2×C4—281no—
626C2×C4—281no—
627C2×C4—281no—
628C2×C4—281no—
629C2×C4—281no—
630C2×C4—281no—
631C2×C4—281no—
632C2×C4—564no—
633C2×C4C4×C22⋊D712yes—
634C2×C4#650212yes—
635C2×C4#650212yes—
636C2×C4C22×C4×D711yescharacteristic
637C2×C4C2×#115711yescharacteristic
638C2×C4C2×D4×D711yescharacteristic
639C2×C4C2×#115911yescharacteristic
640C2×C4D7×#4111yescharacteristic
641C2×C4D7×#4111yescharacteristic
642C8—74no—
643C8—142no—
644C8—142no—
645C8—142no—
646C7#2153511yescharacteristic, complemented, Sylow
647C22—22no—
648C22—22no—
649C22—22no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22—41no—
654C22—282no—
655C22—282no—
656C22—282no—
657C22—561no—
658C22—561no—
659C22—561no—
660C22—561no—
661C22C2×C4×C22⋊D711yescharacteristic
662C22C2×#650211yescharacteristic
663C22#9052311yescharacteristic
664C22#9052611yescharacteristic
665C22#9052811yescharacteristic
666C22#9052811yescharacteristic
667C22#9052911yescharacteristic
668C4—22no—
669C4—22no—
670C4—22no—
671C4—42no—
672C4—42no—
673C4—41no—
674C4—41no—
675C4—81no—
676C4—81no—
677C4—282no—
678C4—561no—
679C4—561no—
680C4C4×#115911yescharacteristic
681C4#9022911yescharacteristic
682C4C4×D4×D711yescharacteristic
683C4#9023811yescharacteristic
684C2—42no—
685C2—562no—
686C2C4×#650211yescharacteristic
687C2#1173999211yescharacteristic
688C2#1174000911yescharacteristic
689C2#1174084311yescharacteristic
690C2#1174086611yescharacteristic
691C2#1174089011yescharacteristic
692C2#1174090411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#2323C2
socleC23×C7C22×D4
prime radicalC2×#6493C22
cosocleC22×C4×C7C24
hypercenter#2323D7
hypocenterC7#21535
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2323

Complements

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

NH ≅ G/Ntype
1. C7×#2323C2semidirect
3. C2×C4×#1143C2semidirect
5. C2×#89769C2semidirect
6. #11729450C2semidirect
7. #11729385C2semidirect
8. #11727433C2semidirect
9. #11727428C2semidirect
10. #11727374C2semidirect
11. #11727369C2semidirect
13. #11727267C2semidirect
14. C4×#6381C2semidirect
15. #11727228C2semidirect
36. #89821C4semidirect
69. C7×C22⋊Q8C2×C4semidirect
107. C2×#1136C2×C4semidirect
124. #6409C2×C4semidirect
133. #6381C2×C4semidirect
137. C4×C7⋊C8D4semidirect
142. #2323D7semidirect
381. C22⋊Q8C4×D7semidirect
646. C7#21535semidirect

Maximal subgroups

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

subgroupindex
C7×#23232
C2×#898212
C2×C4×#11432
#117396812
C2×#897692
#117294502
#117293852
#117274332
#117274282
#117273742
#117273692
#117272692
#117272672
C4×#63812
#117272282
#215357