Finite Group Databasebeta

← #30615914

Subgroups — #30615914

Order 15616.

1126 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840773C211yesmaximal, characteristic, complemented
2C2×#16840752C211yesmaximal, characteristic
3#21462294C211yesmaximal, characteristic
4#21462257C211yesmaximal, characteristic, complemented
5#21461899C212yesmaximal, complemented
6#21461898C212yesmaximal, complemented
7#21461897C212yesmaximal, complemented
8#21461896C212yesmaximal, complemented
9C2×#16840635C211yesmaximal, characteristic, complemented
10#21461487C211yesmaximal, characteristic, complemented
11#417×D61C211yesmaximal, characteristic
12C22×D61⋊C8C2211yescharacteristic
13C2×#14519856C2211yescharacteristic
14C2×#14519856C2211yescharacteristic
15C22×C4⋊#6923C2211yescharacteristic
16#16840773—24no—
17C2×#14519846C2212yes—
18C2×#14519845C2212yes—
19#16840752—24no—
20C2×#14519840C2211yescharacteristic
21C2×#14519840C2211yescharacteristic
22C2×#14519839C2211yescharacteristic
23C2×#14519839C2211yescharacteristic
24(C2×#6923)⋊Q8C2212yes—
25#16840714C2212yes—
26#16840710—22no—
27#16840704—21no—
28#16840704—21no—
29C4⋊C4×#6923—21no—
30C4⋊C4×#6923—21no—
31C4⋊C4×#6923C2212yes—
32C4⋊C4×#6923C2212yes—
33C4×C22⋊#6923—22no—
34#16840635C2212yes—
35#16840635C2212yes—
36(C2×#6923)⋊C8C2212yes—
37(C2×#6923)⋊C8C2212yes—
38C2×#41×D61C2211yescharacteristic
39C2×M16×D61C2211yescharacteristic
40C2×C4⋊C4×D61C2211yescharacteristic
41#16839764C411yescharacteristic, complemented
42#16839763C411yescharacteristic, complemented
43#16839762C412yescomplemented
44#16839761C411yescharacteristic, complemented
45#16839760C412yescomplemented
46#103×D61C2212yes—
47#102×D61C2212yes—
48C61×#417C411yescharacteristic, complemented
49C23×#6923—21no—
50C2×D61⋊C8—22no—
51C2×D61⋊C8—22no—
52C2×D61⋊C8—21no—
53C2×D61⋊C8C2311yescharacteristic
54C2×D61⋊C8C2311yescharacteristic
55C22×#92420—21no—
56#14519856—22no—
57#14519856—22no—
58#14519856—22no—
59#14519856D414yes—
60C2×C4⋊#6923—22no—
61C2×C4⋊#6923—22no—
62C2×C4⋊#6923—21no—
63C2×C4⋊#6923D411yescharacteristic
64C2×C4⋊#6923D411yescharacteristic
65C2×C4⋊#6923C2312yes—
66C2×C4⋊#6923C2311yescharacteristic
67C2×C4⋊#6923C2311yescharacteristic
68C2×C22⋊#6923—21no—
69C2×C22⋊#6923—22no—
70C2×C22⋊#6923—22no—
71C2×C22⋊#6923D412yes—
72C2×C4×#6923—21no—
73C2×C4×#6923—22no—
74C2×C4×#6923—22no—
75C2×C4×#6923C2312yes—
76#14519846—24no—
77#14519845—24no—
78#14519840—22no—
79#14519840—22no—
80#14519839—22no—
81#14519839—22no—
82(C2×#6923)⋊C4—22no—
83(C2×#6923)⋊C4—22no—
84(C2×#6923)⋊C4—22no—
85(C2×#6923)⋊C4—22no—
86C2×#11758226C2×C411yescharacteristic
87C2×#11758222—21no—
88C2×#11758222C2×C411yescharacteristic
89C2×#11758224—21no—
90C2×#11758224C2×C411yescharacteristic
91#41×D61—22no—
92#41×D61—22no—
93#41×D61—22no—
94#41×D61—22no—
95C2×Q8×D61C2311yescharacteristic
96C2×D4×D61—21no—
97C2×D4×D61C2311yescharacteristic
98C22×C4×D61—21no—
99C22×C4×D61—21no—
100C22×C4×D61C2311yescharacteristic
101C2×#11758194C2×C411yescharacteristic
102C2×#11758189C2×C412yes—
103M16×D61—22no—
104M16×D61—22no—
105C2×C8×D61C2312yes—
106C2×C4⋊Dic61C2×C411yescharacteristic
107C2×#11758196—21no—
108C4⋊C4×D61—21no—
109C4⋊C4×D61—21no—
110C4⋊C4×D61C2×C412yes—
111C4⋊C4×D61C2312yes—
112#14519702C2×C412yescomplemented
113#14519701C2×C412yescomplemented
114#14519700C2×C412yescomplemented
115#14519699C2×C412yescomplemented
116#14519698C2×C412yescomplemented
117#14519697C2×C412yescomplemented
118C2×#41×C61C2×C411yescharacteristic
119C2×M16×C61C2×C411yescharacteristic
120C2×C4⋊C4×C61C2×C411yescharacteristic
121#103×C61C2×C412yescomplemented
122#102×C61C2×C412yescomplemented
123C23×D61—21no—
124C23×D61C2×D411yescharacteristic
125C22×#6923—21no—
126C22×#6923—21no—
127C22×#6923—22no—
128C22×#6923—42no—
129C22×#6923—81no—
130C22×#6923—81no—
131C22×#6923C2×D412yes—
132C22×#6923C2×D412yes—
133#41×C61—22no—
134#41×C61—22no—
135C2×Q8×C61C22×C411yescharacteristic
136C2×D4×C61—21no—
137C2×D4×C61C22×C411yescharacteristic
138C22×C4×C61—21no—
139C22×C4×C61—21no—
140C22×C4×C61C22×C411yescharacteristic
141C2×C22⋊D61—21no—
142C2×C22⋊D61—21no—
143C2×C22⋊D61—21no—
144C22×Dic61—21no—
145C22×Dic61—21no—
146C22×Dic61#4111yescharacteristic
147#11758226—22no—
148#11758226—22no—
149Q8×D61—21no—
150Q8×D61—21no—
151Q8×D61—21no—
152Q8×D61—21no—
153#11758224—22no—
154#11758224—22no—
155#11758224—42no—
156#11758224—42no—
157D4×D61—21no—
158D4×D61—21no—
159D4×D61—21no—
160D4×D61—21no—
161D4×D61—42no—
162D4×D61—42no—
163#11758222—22no—
164#11758222—22no—
165#11758222—42no—
166#11758222—42no—
167C2×D244—21no—
168C2×D244C22×C411yescharacteristic
169C2×C4×D61—21no—
170C2×C4×D61—22no—
171C2×C4×D61—21no—
172C2×C4×D61—21no—
173C2×C4×D61—22no—
174C2×C4×D61—42no—
175C2×C4×D61—42no—
176C2×C4×D61—81no—
177C2×C4×D61—81no—
178C2×C4×D61C22×C411yescharacteristic
179C2×C4×D61C2×D412yes—
180C2×C4×D61C2×D411yescharacteristic
181C2×C4×D61#4112yes—
182C2×C4×D61#4112yes—
183C2×C4×D61#4112yes—
184C2×C4×D61#4111yescharacteristic
185C2×C4×D61C2411yescharacteristic
186C2×Dic122—21no—
187C2×Dic122C22×C411yescharacteristic
188C22⋊#6923—24no—
189C22⋊#6923—24no—
190C22⋊#6923—82no—
191C22⋊#6923—82no—
192C2×#92420—21no—
193C2×#92420—21no—
194C2×#92420—42no—
195C4⋊#6923—22no—
196C4⋊#6923—22no—
197C4⋊#6923—22no—
198C4⋊#6923—21no—
199C4⋊#6923—21no—
200C4⋊#6923—22no—
201C4⋊#6923—42no—
202C4⋊#6923C2×D412yes—
203C4⋊#6923C2×D412yes—
204C4×#6923—24no—
205C4×#6923—22no—
206C4×#6923—22no—
207C4×#6923—82no—
208C4×#6923—82no—
209D61⋊C8—21no—
210D61⋊C8—21no—
211D61⋊C8—21no—
212D61⋊C8—21no—
213D61⋊C8—42no—
214M16×C61—22no—
215C2×C8×C61C22×C412yes—
216C4⋊C4×C61—21no—
217C4⋊C4×C61C22×C412yes—
218C4⋊Dic61—21no—
219C4⋊Dic61C22×C412yes—
220#11758196—22no—
221#11758196—22no—
222#11758194—22no—
223C2×#92418C22×C412yes—
224#11758189—24no—
225C8×D61—22no—
226C8×D61—22no—
227C23×C61—21no—
228C23×C61C4×D411yescharacteristic
229C22×D61—21no—
230C22×D61—21no—
231C22×D61—21no—
232C22×D61—21no—
233C22×D61—21no—
234C22×D61—41no—
235C22×D61—41no—
236C22×D61—41no—
237C22×D61—41no—
238C22×D61—41no—
239C22×D61—41no—
240C22×D61C4×D411yescharacteristic
241C22×D61#12112yes—
242C22×D61#12312yes—
243C22×D61C22×D411yescharacteristic
244C2×#6923—22no—
245C2×#6923—22no—
246C2×#6923—22no—
247C2×#6923—22no—
248C2×#6923—22no—
249C2×#6923—22no—
250C2×#6923—22no—
251C2×#6923—22no—
252C2×#6923—41no—
253C2×#6923—41no—
254C2×#6923—41no—
255C2×#6923—41no—
256C2×#6923—42no—
257C2×#6923—42no—
258C2×#6923—42no—
259C2×#6923—84no—
260Q8×C61—21no—
261Q8×C61—21no—
262D4×C61—21no—
263D4×C61—21no—
264D4×C61—42no—
265C2×C4×C61—22no—
266C2×C4×C61—21no—
267C2×C4×C61—42no—
268C2×C4×C61—81no—
269C2×C4×C61#11712yes—
270C2×C4×C61C4×D412yes—
271C2×C4×C61C4×D411yescharacteristic
272C2×C4×C61C23×C411yescharacteristic
273C22⋊D61—42no—
274C22⋊D61—42no—
275C22⋊D61—41no—
276C22⋊D61—41no—
277C2×Dic61—22no—
278C2×Dic61—21no—
279C2×Dic61—42no—
280C2×Dic61—81no—
281C2×Dic61C4×D411yescharacteristic
282C2×Dic61#12412yes—
283C2×Dic61#12612yes—
284C2×Dic61C2×#4111yescharacteristic
285D244—21no—
286D244—21no—
287D244—42no—
288C4×D61—41no—
289C4×D61—41no—
290C4×D61—42no—
291C4×D61—42no—
292C4×D61—42no—
293C4×D61—42no—
294C4×D61—82no—
295C4×D61#11712yes—
296C4×D61C4×D412yes—
297C4×D61#12112yes—
298C4×D61#12312yes—
299C4×D61#12412yes—
300C4×D61#12612yes—
301C4×D61C22×D411yescharacteristic
302C4×D61C2×#4111yescharacteristic
303C4×D61C2×#4111yescharacteristic
304C4×D61C2×#4111yescharacteristic
305Dic122—21no—
306Dic122—21no—
307Dic122—41no—
308Dic122—41no—
309#92420—41no—
310#92420—41no—
311C8×C61—22no—
312#92418—22no—
313#21062—611nomaximal, Sylow
314C22×C61—21no—
315C22×C61—21no—
316C22×C61—41no—
317C22×C61—41no—
318C22×C61—41no—
319C22×C61#38812yes—
320C22×C61C2×C4×D411yescharacteristic
321C2×D61—21no—
322C2×D61—21no—
323C2×D61—22no—
324C2×D61—22no—
325C2×D61—22no—
326C2×D61—22no—
327C2×D61—41no—
328C2×D61—41no—
329C2×D61—41no—
330C2×D61—81no—
331C2×D61—81no—
332C2×D61—81no—
333C2×D61—81no—
334C2×D61#38812yes—
335C2×D61C2×#12111yescharacteristic
336C2×D61C2×#12311yescharacteristic
337C2×D61#57611yescharacteristic
338C2×D61#57711yescharacteristic
339C2×D61#57711yescharacteristic
340C2×D61#57811yescharacteristic
341#6923—42no—
342#6923—42no—
343#6923—42no—
344#6923—42no—
345#6923—82no—
346C4×C61—42no—
347C4×C61—41no—
348C4×C61#38812yes—
349C4×C61C2×#11711yescharacteristic
350C4×C61C2×C4×D411yescharacteristic
351Dic61—42no—
352Dic61—41no—
353Dic61#38812yes—
354Dic61C2×#12411yescharacteristic
355Dic61C2×#12611yescharacteristic
356C2×#428—611no—
357C2×#417—611no—
358C2×#416—611no—
359#2311—611no—
360#2274—611no—
361#1928—612no—
362#1927—612no—
363#1926—612no—
364#1925—612no—
365C2×#340—611no—
366#1729—611no—
367C2×C61—22no—
368C2×C61—81no—
369C2×C61C2×#38811yescharacteristic
370C2×C61#294611yescharacteristic
371C2×C61#294711yescharacteristic
372D61—22no—
373D61—81no—
374D61#304511yescharacteristic
375D61#304611yescharacteristic
376D61#309811yescharacteristic
377D61#309911yescharacteristic
378C22×#41—611no—
379C22×M16—611no—
380C23×C8—611no—
381C2×#117—611no—
382C2×#117—611no—
383C22×C4⋊C4—611no—
384C22×C4⋊C4—611no—
385#428—1224no—
386C2×#107—612no—
387C2×#106—612no—
388#417—611no—
389#417—611no—
390#417—611no—
391#417—612no—
392#417—612no—
393#417#692311yescharacteristic, complemented
394#416—1224no—
395C2×#103—612no—
396C2×#103—611no—
397C2×#103—611no—
398C2×#102—612no—
399C2×#102—611no—
400C2×#102—611no—
401#391—612no—
402#390—612no—
403#386—1222no—
404#380—1221no—
405#380—1221no—
406C4×C4⋊C4—612no—
407C4×C4⋊C4—612no—
408C4×C4⋊C4—1221no—
409C4×C4⋊C4—1221no—
410C4×C22⋊C4—1222no—
411#340—612no—
412#340—612no—
413#336—612no—
414#336—612no—
415C61#2106211yescharacteristic, complemented, Sylow
416C2×#41—611no—
417C2×#41—611no—
418C2×#41—611no—
419C2×#41—1221no—
420C2×#41—1221no—
421C2×#41—1222no—
422C2×#41—1222no—
423C2×#41—1222no—
424C2×#41—1222no—
425C2×#41C2×#692311yescharacteristic
426C22×Q8—611no—
427C22×D4—611no—
428C22×D4—1221no—
429C23×C4—611no—
430C23×C4—1221no—
431C23×C4—1221no—
432C23×C4—1221no—
433C2×M16—611no—
434C2×M16—612no—
435C2×M16—1222no—
436C2×M16—1222no—
437C2×M16C2×#692311yescharacteristic
438C22×C8—612no—
439C22×C8—611no—
440C22×C8—611no—
441C22×C8—1221no—
442C22×C8—1222no—
443C22×C8—1221no—
444C22×C8—1222no—
445#117—614no—
446#117—1222no—
447#117—1222no—
448#117—1222no—
449C2×C4⋊C4—611no—
450C2×C4⋊C4—611no—
451C2×C4⋊C4—611no—
452C2×C4⋊C4—612no—
453C2×C4⋊C4—612no—
454C2×C4⋊C4—611no—
455C2×C4⋊C4—611no—
456C2×C4⋊C4—612no—
457C2×C4⋊C4—1221no—
458C2×C4⋊C4—1221no—
459C2×C4⋊C4—1221no—
460C2×C4⋊C4—1222no—
461C2×C4⋊C4—1222no—
462C2×C4⋊C4—1221no—
463C2×C4⋊C4C2×#692311yescharacteristic
464C2×C22⋊C4—612no—
465C2×C22⋊C4—1221no—
466C2×C22⋊C4—1222no—
467C2×C22⋊C4—1222no—
468C2×C42—612no—
469C2×C42—1221no—
470C2×C42—1222no—
471C2×C42—1222no—
472#107—1224no—
473#106—1224no—
474#103—612no—
475#103—612no—
476#103—612no—
477#103—1222no—
478#103—1222no—
479#103C2×#692312yescomplemented
480#102—612no—
481#102—612no—
482#102—612no—
483#102—1222no—
484#102—1222no—
485#102C2×#692312yescomplemented
486#95—1222no—
487#95—1222no—
488#95—1222no—
489#95—1222no—
490C24—611no—
491C24—1221no—
492#41—22no—
493#41—22no—
494#41—1222no—
495#41—1222no—
496#41—1222no—
497#41—1222no—
498#41—1222no—
499#41—1222no—
500#41—2442no—
501#41—2442no—
502#41—2442no—
503#41—2442no—
504C2×Q8—611no—
505C2×Q8—1221no—
506C2×Q8—1221no—
507C2×Q8—1221no—
508C2×Q8—1221no—
509C2×Q8—1221no—
510C2×Q8C22×#692311yescharacteristic
511C2×D4—21no—
512C2×D4—611no—
513C2×D4—1221no—
514C2×D4—1221no—
515C2×D4—1221no—
516C2×D4—1221no—
517C2×D4—1221no—
518C2×D4—1221no—
519C2×D4—1221no—
520C2×D4—1221no—
521C2×D4—2442no—
522C2×D4—2442no—
523C2×D4C22×#692311yescharacteristic
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—611no—
527C22×C4—612no—
528C22×C4—612no—
529C22×C4—611no—
530C22×C4—612no—
531C22×C4—611no—
532C22×C4—612no—
533C22×C4—611no—
534C22×C4—611no—
535C22×C4—612no—
536C22×C4—612no—
537C22×C4—1221no—
538C22×C4—1222no—
539C22×C4—1221no—
540C22×C4—1222no—
541C22×C4—1221no—
542C22×C4—1221no—
543C22×C4—1221no—
544C22×C4—1221no—
545C22×C4—1221no—
546C22×C4—1222no—
547C22×C4—4881no—
548C22×C4—4881no—
549C22×C4—4881no—
550C22×C4—4881no—
551C22×C4—2442no—
552C22×C4—2442no—
553C22×C4—2442no—
554C22×C4C22×#692311yescharacteristic
555M16—22no—
556M16—1224no—
557M16—1222no—
558C2×C8—612no—
559C2×C8—1222no—
560C2×C8—1222no—
561C2×C8—1221no—
562C2×C8—1221no—
563C2×C8—1221no—
564C2×C8—1221no—
565C2×C8—1221no—
566C2×C8—1221no—
567C2×C8—2442no—
568C2×C8—2442no—
569C2×C8C22×#692312yes—
570C4⋊C4—21no—
571C4⋊C4—612no—
572C4⋊C4—612no—
573C4⋊C4—612no—
574C4⋊C4—1222no—
575C4⋊C4—1222no—
576C4⋊C4—1222no—
577C4⋊C4—1222no—
578C4⋊C4—1221no—
579C4⋊C4—1221no—
580C4⋊C4—1222no—
581C4⋊C4—1222no—
582C4⋊C4—1221no—
583C4⋊C4—2442no—
584C4⋊C4C22×#692312yes—
585C22⋊C4—1224no—
586C22⋊C4—1224no—
587C22⋊C4—4882no—
588C22⋊C4—4882no—
589C42—1222no—
590C42—1222no—
591C42—1224no—
592C42—4882no—
593C42—4882no—
594C23—21no—
595C23—611no—
596C23—612no—
597C23—612no—
598C23—611no—
599C23—1221no—
600C23—1221no—
601C23—1221no—
602C23—1221no—
603C23—1221no—
604C23—2441no—
605C23—2441no—
606C23—2441no—
607C23—2441no—
608C23—2441no—
609C23—2441no—
610C23D4×#692311yescharacteristic
611Q8—21no—
612Q8—21no—
613Q8—1221no—
614Q8—1221no—
615Q8—2441no—
616Q8—2441no—
617D4—21no—
618D4—21no—
619D4—42no—
620D4—1221no—
621D4—1221no—
622D4—2442no—
623D4—2441no—
624D4—2441no—
625D4—2442no—
626D4—2442no—
627C2×C4—22no—
628C2×C4—21no—
629C2×C4—42no—
630C2×C4—81no—
631C2×C4—612no—
632C2×C4—612no—
633C2×C4—611no—
634C2×C4—611no—
635C2×C4—612no—
636C2×C4—612no—
637C2×C4—612no—
638C2×C4—612no—
639C2×C4—612no—
640C2×C4—611no—
641C2×C4—611no—
642C2×C4—612no—
643C2×C4—611no—
644C2×C4—611no—
645C2×C4—1222no—
646C2×C4—1222no—
647C2×C4—1222no—
648C2×C4—1222no—
649C2×C4—1222no—
650C2×C4—1222no—
651C2×C4—1222no—
652C2×C4—1222no—
653C2×C4—1222no—
654C2×C4—1221no—
655C2×C4—4882no—
656C2×C4—4884no—
657C2×C4—4881no—
658C2×C4—2442no—
659C2×C4—2442no—
660C2×C4—2442no—
661C2×C4—2441no—
662C2×C4—2441no—
663C2×C4—2442no—
664C2×C4—2442no—
665C2×C4—2442no—
666C2×C4—2442no—
667C2×C4—2441no—
668C2×C4—2441no—
669C2×C4—2441no—
670C2×C4—2441no—
671C2×C4—2442no—
672C2×C4#1451985612yes—
673C2×C4D4×#692311yescharacteristic
674C2×C4D4×#692312yes—
675C2×C4C23×#692311yescharacteristic
676C8—22no—
677C8—1222no—
678C8—2441no—
679C8—2441no—
680C22—21no—
681C22—21no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—611no—
686C22—611no—
687C22—611no—
688C22—611no—
689C22—611no—
690C22—611no—
691C22—612no—
692C22—1222no—
693C22—1222no—
694C22—1222no—
695C22—1222no—
696C22—1221no—
697C22—1221no—
698C22—4881no—
699C22—4881no—
700C22—4881no—
701C22—4881no—
702C22—2441no—
703C22—2441no—
704C22—2441no—
705C22#1684071212yes—
706C22C2×D4×#692311yescharacteristic
707C4—41no—
708C4—42no—
709C4—611no—
710C4—611no—
711C4—612no—
712C4—4882no—
713C4—2442no—
714C4—2442no—
715C4—2442no—
716C4—2442no—
717C4—2441no—
718C4—2442no—
719C4#1684071212yes—
720C4C2×#1451985611yescharacteristic
721C4C2×D4×#692311yescharacteristic
722C2—22no—
723C2—81no—
724C2—611no—
725C2—611no—
726C2—611no—
727C2—611no—
728C2—1222no—
729C2—4881no—
730C2C2×#1684071211yescharacteristic
731C2#2146257611yescharacteristic
732C2#2146257711yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#417C4
socleC22×C61C2×C4×D4
prime radicalC2×#41×D61C22
cosocleC2×C4×D61C24
hypercenter#417#6923
hypocenterC61#21062
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. C2×#16840773C2semidirect
4. #21462257C2semidirect
5. #21461899C2semidirect
6. #21461898C2semidirect
7. #21461897C2semidirect
8. #21461896C2semidirect
9. C2×#16840635C2semidirect
10. #21461487C2semidirect
41. #16839764C4semidirect
42. #16839763C4semidirect
43. #16839762C4semidirect
44. #16839761C4semidirect
45. #16839760C4semidirect
48. C61×#417C4semidirect
112. #14519702C2×C4semidirect
113. #14519701C2×C4semidirect
114. #14519700C2×C4semidirect
115. #14519699C2×C4semidirect
116. #14519698C2×C4semidirect
117. #14519697C2×C4semidirect
121. #103×C61C2×C4semidirect
122. #102×C61C2×C4semidirect
393. #417#6923semidirect
415. C61#21062semidirect
479. #103C2×#6923semidirect
485. #102C2×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168407732
C2×#168407522
#214622942
#214622572
#214618992
#214618982
#214618972
#214618962
C2×#168406352
#214614872
#417×D612
#2106261