Subgroups — #13092193

Order 1472.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₈×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃⋊C₁₆	C₂	1	2	yes	maximal
3	C₂×C₈×C₂₃	C₄	1	1	yes	characteristic
4	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
5	C₄²×C₂₃	C₄	1	1	yes	characteristic
6	C₂₃⋊C₁₆	C₄	1	4	yes	complemented
7	C₂×C₄×C₂₃	C₈	1	2	yes	—
8	C₂×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
9	C₈×C₂₃	C₈	1	2	yes	—
10	C₈×C₂₃	C₂×C₄	1	2	yes	—
11	C₂²×C₂₃	C₂×C₈	1	1	yes	characteristic
12	C₄×C₂₃	—	2	2	no	—
13	C₄×C₂₃	C₄²	1	1	yes	characteristic
14	C₄×C₂₃	C₂×C₈	1	1	yes	characteristic
15	#346	—	23	1	no	maximal, Sylow
16	C₂×C₂₃	C₄×C₈	1	1	yes	characteristic
17	C₂×C₂₃	M₃₂	1	2	yes	—
18	C₂×C₁₆	—	23	2	no	—
19	C₄×C₈	D₂₃	1	1	yes	characteristic
20	C₂₃	#346	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₈	Dic₂₃	1	1	yes	characteristic
22	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
23	C₄²	Dic₂₃	1	1	yes	characteristic
24	C₁₆	—	23	4	no	—
25	C₂×C₄	C₂₃⋊C₈	1	2	yes	—
26	C₂×C₄	C₂×Dic₂₃	1	1	yes	characteristic
27	C₈	C₂₃⋊C₈	1	2	yes	—
28	C₈	C₄×D₂₃	1	2	yes	—
29	C₂²	C₂×C₂₃⋊C₈	1	1	yes	characteristic
30	C₄	—	2	2	no	—
31	C₄	C₂×C₂₃⋊C₈	1	1	yes	characteristic
32	C₄	C₄×Dic₂₃	1	1	yes	characteristic
33	C₂	C₄×C₂₃⋊C₈	1	1	yes	characteristic
34	C₂	#10624994	1	2	yes	—

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

N	H ≅ G/N	type
6. C₂₃⋊C₁₆	C₄	semidirect
20. C₂₃	#346	semidirect

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