Subgroups — #73316

Order 384.

418 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄³	C₂	1	1	yes	maximal, characteristic, complemented
2	#4940	C₂	1	7	yes	maximal
3	#4933	C₂	1	7	yes	maximal, complemented
4	#2865	—	3	1	no	maximal, Sylow
5	C₂×C₃×C₄²	C₂²	1	7	yes	—
6	C₂×(C₂×D₃)⋊C₄	C₂²	1	7	yes	—
7	C₂×Dic₃⋊C₄	C₂²	1	7	yes	—
8	C₃⋊#95	C₂²	1	14	yes	—
9	#388	—	3	7	no	—
10	#387	—	3	7	no	—
11	C₄³	D₃	1	1	yes	characteristic, complemented
12	C₂³×D₃	C₂³	1	1	yes	characteristic
13	C₂²×C₃×C₄	C₂³	1	7	yes	—
14	C₂²×Dic₃	C₂³	1	7	yes	—
15	C₃×C₄²	—	2	14	no	—
16	(C₂×D₃)⋊C₄	—	2	14	no	—
17	Dic₃⋊C₄	—	2	14	no	—
18	C₂×C₄⋊C₄	—	3	7	no	—
19	C₂×C₂²⋊C₄	—	3	7	no	—
20	C₂×C₄²	C₂×D₃	1	7	yes	—
21	#95	—	3	14	no	—
22	C₂³×C₃	C₂⁴	1	1	yes	characteristic
23	C₂²×D₃	—	2	7	no	—
24	C₂×C₃×C₄	—	2	14	no	—
25	C₂×C₃×C₄	#41	1	14	yes	—
26	C₂×Dic₃	—	2	14	no	—
27	C₂×Dic₃	—	2	7	no	—
28	C₂⁴	—	3	1	no	—
29	C₂²×C₄	—	3	7	no	—
30	C₂²×C₄	C₂²×D₃	1	7	yes	—
31	C₄⋊C₄	—	6	14	no	—
32	C₂²⋊C₄	—	6	14	no	—
33	C₄²	—	2	14	no	—
34	C₂²×C₃	C₂×#41	1	7	yes	—
35	C₂×D₃	—	4	7	no	—
36	C₃×C₄	—	2	14	no	—
37	Dic₃	—	4	7	no	—
38	C₂³	—	6	7	no	—
39	C₂³	C₂³×D₃	1	1	yes	characteristic
40	C₂×C₄	—	2	14	no	—
41	C₂×C₄	—	6	7	no	—
42	C₂×C₄	—	6	14	no	—
43	C₂×C₄	#235	1	14	yes	—
44	C₂×C₃	#529	1	7	yes	—
45	D₃	—	8	1	no	—
46	C₂²	—	12	7	no	—
47	C₂²	C₂×#235	1	7	yes	—
48	C₄	—	2	14	no	—
49	C₄	—	12	7	no	—
50	C₃	#2865	1	1	yes	characteristic, complemented, Sylow
51	C₂	—	24	1	no	—
52	C₂	#5479	1	7	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.