Subgroups — #13092247

Order 1472.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic
2	#10625001	C₂	1	2	yes	maximal
3	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
4	#67267	—	2	2	no	—
5	C₁₆×C₂₃	C₄	1	2	yes	—
6	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
7	C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
8	C₈×C₂₃	Q₈	1	1	yes	characteristic
9	C₂₃⋊C₈	—	4	2	no	—
10	C₂²×C₂₃	Q₁₆	1	1	yes	characteristic
11	C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
12	C₄×C₂₃	D₈	1	1	yes	characteristic
13	#368	—	23	1	no	maximal, Sylow
14	C₂×C₂₃	—	2	1	no	—
15	C₂×C₂₃	#107	1	1	yes	characteristic
16	C₂×C₁₆	D₂₃	1	1	yes	characteristic
17	#108	—	23	2	no	—
18	C₂₃	#368	1	1	yes	characteristic, complemented, Sylow
19	M₁₆	—	46	2	no	—
20	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
21	C₁₆	Dic₂₃	1	2	yes	—
22	C₂×C₄	D₉₂	1	1	yes	characteristic
23	C₈	—	92	2	no	—
24	C₈	Dic₄₆	1	1	yes	characteristic
25	C₈	C₂×Dic₂₃	1	1	yes	characteristic
26	C₂²	Dic₉₂	1	1	yes	characteristic
27	C₄	D₁₈₄	1	1	yes	characteristic
28	C₄	C₄⋊Dic₂₃	1	1	yes	characteristic
29	C₂	—	2	1	no	—
30	C₂	#10625000	1	1	yes	characteristic

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

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

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