Subgroups — #13092262

Order 1472.

178 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Dic₂₃	C₂	1	3	yes	maximal
2	C₂₃×#95	C₂	1	1	yes	maximal, characteristic
3	C₂₃⋊#95	C₂	1	3	yes	maximal
4	C₂²×C₄×C₂₃	C₂²	1	3	yes	—
5	C₂²×Dic₂₃	C₂²	1	3	yes	—
6	C₂²×Dic₂₃	C₂²	1	1	yes	characteristic
7	C₄×Dic₂₃	C₄	1	12	yes	complemented
8	C₂³×C₂₃	C₂³	1	1	yes	characteristic
9	C₂×C₄×C₂₃	—	2	6	no	—
10	C₂×C₄×C₂₃	C₂×C₄	1	6	yes	—
11	C₂×Dic₂₃	—	2	3	no	—
12	C₂×Dic₂₃	—	2	3	no	—
13	C₂×Dic₂₃	C₂×C₄	1	6	yes	—
14	C₂×Dic₂₃	C₂×C₄	1	6	yes	—
15	C₂²×C₂₃	C₂²×C₄	1	3	yes	—
16	C₂²×C₂₃	#41	1	3	yes	—
17	C₂²×C₂₃	#41	1	1	yes	characteristic
18	C₄×C₂₃	—	2	6	no	—
19	Dic₂₃	—	2	6	no	—
20	Dic₂₃	C₄²	1	4	yes	—
21	#376	—	23	1	no	maximal, Sylow
22	C₂×C₂₃	C₂×C₄²	1	1	yes	characteristic
23	C₂×C₂₃	#117	1	3	yes	—
24	C₂×C₂₃	#117	1	3	yes	—
25	C₂×C₄²	—	23	3	no	—
26	#95	—	23	3	no	—
27	#95	D₂₃	1	1	yes	characteristic
28	C₂₃	#376	1	1	yes	characteristic, complemented, Sylow
29	C₂²×C₄	—	23	1	no	—
30	C₂²×C₄	—	23	3	no	—
31	C₂²×C₄	C₂×D₂₃	1	3	yes	—
32	C₄²	—	23	12	no	—
33	C₂³	C₂²×D₂₃	1	1	yes	characteristic
34	C₂×C₄	—	2	6	no	—
35	C₂×C₄	—	23	6	no	—
36	C₂×C₄	—	23	6	no	—
37	C₂×C₄	—	46	3	no	—
38	C₂×C₄	—	46	3	no	—
39	C₂×C₄	C₄×D₂₃	1	6	yes	—
40	C₂²	C₂×C₄×D₂₃	1	3	yes	—
41	C₂²	#67290	1	3	yes	—
42	C₂²	#67292	1	1	yes	characteristic
43	C₄	—	2	6	no	—
44	C₄	—	23	4	no	—
45	C₄	—	46	6	no	—
46	C₂	C₄²×D₂₃	1	1	yes	characteristic
47	C₂	#10625048	1	3	yes	—
48	C₂	#10625063	1	3	yes	—

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

N	H ≅ G/N	type
7. C₄×Dic₂₃	C₄	semidirect
28. C₂₃	#376	semidirect

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