Subgroups — #28383414

Order 14272.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₂₃⋊C₃₂	C₂	1	2	yes	maximal, complemented
2	C₂×C₁₆×C₂₂₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×C₂₂₃	C₄	1	1	yes	characteristic
4	C₁₆×C₂₂₃	C₄	1	1	yes	characteristic
5	C₁₆×C₂₂₃	C₂²	1	1	yes	characteristic
6	C₂×C₄×C₂₂₃	C₈	1	1	yes	characteristic
7	C₈×C₂₂₃	C₈	1	1	yes	characteristic
8	C₈×C₂₂₃	C₂×C₄	1	1	yes	characteristic
9	C₂²×C₂₂₃	C₁₆	1	1	yes	characteristic
10	C₄×C₂₂₃	C₁₆	1	1	yes	characteristic
11	C₄×C₂₂₃	C₂×C₈	1	1	yes	characteristic
12	C₂×C₂₂₃	—	2	1	no	—
13	C₂×C₂₂₃	C₂×C₁₆	1	1	yes	characteristic
14	C₂₂₃	M₆₄	1	1	yes	characteristic, complemented, Sylow
15	M₆₄	—	223	1	no	maximal, Sylow
16	C₂×C₁₆	D₂₂₃	1	1	yes	characteristic
17	C₃₂	—	223	2	no	—
18	C₂×C₈	Dic₂₂₃	1	1	yes	characteristic
19	C₁₆	Dic₂₂₃	1	1	yes	characteristic
20	C₁₆	C₂×D₂₂₃	1	1	yes	characteristic
21	C₂×C₄	C₂₂₃⋊C₈	1	1	yes	characteristic
22	C₈	C₂₂₃⋊C₈	1	1	yes	characteristic
23	C₈	C₂×Dic₂₂₃	1	1	yes	characteristic
24	C₂²	C₂₂₃⋊C₁₆	1	1	yes	characteristic
25	C₄	C₂₂₃⋊C₁₆	1	1	yes	characteristic
26	C₄	C₂×C₂₂₃⋊C₈	1	1	yes	characteristic
27	C₂	—	2	1	no	—
28	C₂	C₂×C₂₂₃⋊C₁₆	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. C₂₂₃⋊C₃₂	C₂	semidirect
14. C₂₂₃	M₆₄	semidirect

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