Subgroups — #37557913

Order 23776.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊Dic₇₄₃	C₂	1	2	yes	maximal
2	C₂×C₈×C₇₄₃	C₂	1	1	yes	maximal, characteristic
3	C₂×Dic₇₄₃	—	2	2	no	—
4	C₂×C₄×C₇₄₃	C₂²	1	1	yes	characteristic
5	C₈×C₇₄₃	C₄	1	2	yes	complemented
6	C₂²×C₇₄₃	D₄	1	1	yes	characteristic
7	C₄×C₇₄₃	C₂×C₄	1	1	yes	characteristic
8	C₄×C₇₄₃	Q₈	1	1	yes	characteristic
9	Dic₇₄₃	—	4	2	no	—
10	C₂×C₇₄₃	C₄⋊C₄	1	1	yes	characteristic
11	C₂×C₇₄₃	D₈	1	1	yes	characteristic
12	C₂×C₇₄₃	Q₁₆	1	1	yes	characteristic
13	C₇₄₃	#107	1	1	yes	characteristic, complemented, Sylow
14	#107	—	743	1	no	maximal, Sylow
15	C₂×C₈	D₇₄₃	1	1	yes	characteristic
16	C₄⋊C₄	—	743	2	no	—
17	C₂×C₄	—	1486	2	no	—
18	C₂×C₄	C₂×D₇₄₃	1	1	yes	characteristic
19	C₈	Dic₇₄₃	1	2	yes	complemented
20	C₂²	D₂₉₇₂	1	1	yes	characteristic
21	C₄	—	2972	2	no	—
22	C₄	C₂×Dic₇₄₃	1	1	yes	characteristic
23	C₄	Dic₁₄₈₆	1	1	yes	characteristic
24	C₂	C₄⋊Dic₇₄₃	1	1	yes	characteristic
25	C₂	D₅₉₄₄	1	1	yes	characteristic
26	C₂	Dic₂₉₇₂	1	1	yes	characteristic

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

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