Subgroups — #68062

Order 384.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#4695	C₂	1	6	yes	maximal, complemented
2	C₃×C₈²	C₂	1	1	yes	maximal, characteristic, complemented
3	#1712	—	3	1	no	maximal, Sylow
4	C₂×D₂₄	—	2	12	no	—
5	#874	C₂²	1	4	yes	—
6	C₃×C₄×C₈	C₂²	1	3	yes	—
7	#493	—	3	6	no	—
8	C₈²	D₃	1	1	yes	characteristic, complemented
9	C₂×D₁₂	—	2	12	no	—
10	C₂×C₃×C₈	D₄	1	6	yes	—
11	C₃×C₄²	C₂³	1	1	yes	characteristic
12	D₂₄	—	4	24	no	—
13	C₂×D₈	—	6	12	no	—
14	#127	—	3	4	no	—
15	C₄×C₈	C₂×D₃	1	3	yes	—
16	C₂²×D₃	—	4	4	no	—
17	C₂×C₃×C₄	C₂×D₄	1	3	yes	—
18	D₁₂	—	4	24	no	—
19	C₃×C₈	D₈	1	12	yes	complemented
20	C₂×D₄	—	6	12	no	—
21	D₈	—	12	24	no	—
22	C₂×C₈	D₁₂	1	6	yes	—
23	C₄²	C₂²×D₃	1	1	yes	characteristic
24	C₂²×C₃	#127	1	1	yes	characteristic
25	C₂×D₃	—	8	12	no	—
26	C₃×C₄	C₂×D₈	1	6	yes	—
27	C₂³	—	12	4	no	—
28	D₄	—	12	24	no	—
29	C₂×C₄	C₂×D₁₂	1	3	yes	—
30	C₈	D₂₄	1	12	yes	complemented
31	C₂×C₃	#493	1	3	yes	—
32	D₃	—	16	4	no	—
33	C₂²	—	24	12	no	—
34	C₂²	#874	1	1	yes	characteristic
35	C₄	C₂×D₂₄	1	6	yes	—
36	C₃	#1712	1	1	yes	characteristic, complemented, Sylow
37	C₂	—	48	4	no	—
38	C₂	#4695	1	3	yes	—

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

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