Subgroups — #13092246

Order 1472.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#108	C₂	1	1	yes	maximal, characteristic
2	#10625001	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	M₁₆×C₂₃	—	2	1	no	—
5	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
6	#67267	—	2	1	no	—
7	C₂₃⋊C₁₆	C₄	1	2	yes	—
8	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
9	C₈×C₂₃	—	4	1	no	—
10	C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
11	C₈×C₂₃	Q₈	1	1	yes	characteristic
12	C₂₃⋊C₈	—	4	1	no	—
13	C₂²×C₂₃	Q₁₆	1	1	yes	characteristic
14	C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₂₃	D₈	1	1	yes	characteristic
16	#368	—	23	1	no	maximal, Sylow
17	C₂×C₂₃	—	2	1	no	—
18	C₂×C₂₃	#107	1	1	yes	characteristic
19	C₂×C₁₆	—	23	1	no	—
20	#108	—	23	1	no	—
21	#108	D₂₃	1	1	yes	characteristic
22	C₂₃	#368	1	1	yes	characteristic, complemented, Sylow
23	M₁₆	—	2	1	no	—
24	M₁₆	—	46	1	no	—
25	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
26	C₁₆	—	23	2	no	—
27	C₂×C₄	C₂²⋊D₂₃	1	1	yes	characteristic
28	C₈	—	4	1	no	—
29	C₈	—	92	1	no	—
30	C₈	Dic₄₆	1	1	yes	characteristic
31	C₈	C₄×D₂₃	1	1	yes	characteristic
32	C₂²	#67275	1	1	yes	characteristic
33	C₄	Dic₂₃⋊C₄	1	1	yes	characteristic
34	C₄	#67272	1	1	yes	characteristic
35	C₂	—	2	1	no	—
36	C₂	#10624989	1	1	yes	characteristic

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

N	H ≅ G/N	type
22. C₂₃	#368	semidirect

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