Subgroups — #67437

Order 384.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₈²	C₂	1	1	yes	maximal, characteristic
2	C₄×C₃⋊C₁₆	C₂	1	2	yes	maximal
3	#1311	—	3	1	no	maximal, Sylow
4	C₃×C₄×C₈	C₄	1	2	yes	—
5	C₃×C₄×C₈	C₂²	1	1	yes	characteristic
6	C₂×C₃⋊C₁₆	C₄	1	4	yes	—
7	C₄×C₁₆	—	3	2	no	—
8	C₈²	D₃	1	1	yes	characteristic
9	C₂×C₃×C₈	C₈	1	4	yes	—
10	C₂×C₃×C₈	C₂×C₄	1	2	yes	—
11	C₃×C₄²	C₂×C₄	1	1	yes	characteristic
12	C₃⋊C₁₆	C₈	1	8	yes	complemented
13	C₂×C₁₆	—	3	4	no	—
14	C₄×C₈	Dic₃	1	2	yes	—
15	C₄×C₈	C₂×D₃	1	1	yes	characteristic
16	C₂×C₃×C₄	C₄²	1	1	yes	characteristic
17	C₂×C₃×C₄	C₂×C₈	1	2	yes	—
18	C₃×C₈	—	2	4	no	—
19	C₃×C₈	C₂×C₈	1	4	yes	—
20	C₂×C₈	C₃⋊C₈	1	4	yes	—
21	C₂×C₈	C₄×D₃	1	2	yes	—
22	C₄²	C₂×Dic₃	1	1	yes	characteristic
23	C₁₆	—	3	8	no	—
24	C₂²×C₃	C₄×C₈	1	1	yes	characteristic
25	C₃×C₄	C₄×C₈	1	2	yes	—
26	C₃×C₄	M₃₂	1	4	yes	—
27	C₂×C₄	C₂×C₃⋊C₈	1	2	yes	—
28	C₂×C₄	C₄×Dic₃	1	1	yes	characteristic
29	C₈	—	2	4	no	—
30	C₈	D₃×C₈	1	4	yes	—
31	C₂×C₃	C₈²	1	1	yes	characteristic
32	C₂×C₃	#346	1	2	yes	—
33	C₂²	C₄×C₃⋊C₈	1	1	yes	characteristic
34	C₄	#812	1	4	yes	—
35	C₄	C₈×Dic₃	1	2	yes	—
36	C₃	#1311	1	1	yes	characteristic, complemented, Sylow
37	C₂	C₈×C₃⋊C₈	1	1	yes	characteristic
38	C₂	#4461	1	2	yes	—

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

N	H ≅ G/N	type
12. C₃⋊C₁₆	C₈	semidirect
36. C₃	#1311	semidirect

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