Subgroups — #376×C₃₈₉ #38733607

Order 24896.

178 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×C₃₈₉	C₂	1	3	yes	maximal
2	#95×C₃₈₉	C₂	1	4	yes	maximal
3	C₂²×C₄×C₃₈₉	C₂²	1	6	yes	—
4	C₂²×C₄×C₃₈₉	C₂²	1	1	yes	characteristic
5	C₄²×C₃₈₉	C₄	1	12	yes	complemented
6	C₂³×C₃₈₉	C₂³	1	1	yes	characteristic
7	C₂×C₄×C₃₈₉	—	2	12	no	—
8	C₂×C₄×C₃₈₉	C₂×C₄	1	12	yes	—
9	C₂×C₄×C₃₈₉	C₂×C₄	1	6	yes	—
10	C₂²×C₃₈₉	C₂²×C₄	1	3	yes	—
11	C₂²×C₃₈₉	#41	1	4	yes	—
12	C₄×C₃₈₉	—	2	12	no	—
13	C₄×C₃₈₉	C₄²	1	4	yes	—
14	C₂×C₃₈₉	C₂×C₄²	1	1	yes	characteristic
15	C₂×C₃₈₉	#117	1	6	yes	—
16	C₃₈₉	#376	1	1	yes	characteristic, direct product factor, Sylow
17	#376	C₃₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
18	C₂×C₄²	C₂×C₃₈₉	1	3	yes	—
19	#95	C₂×C₃₈₉	1	4	yes	—
20	C₂²×C₄	C₂²×C₃₈₉	1	6	yes	—
21	C₂²×C₄	C₂²×C₃₈₉	1	1	yes	characteristic
22	C₄²	C₄×C₃₈₉	1	12	yes	complemented
23	C₂³	C₂³×C₃₈₉	1	1	yes	characteristic
24	C₂×C₄	—	2	12	no	—
25	C₂×C₄	C₂×C₄×C₃₈₉	1	12	yes	—
26	C₂×C₄	C₂×C₄×C₃₈₉	1	6	yes	—
27	C₂²	C₂²×C₄×C₃₈₉	1	3	yes	—
28	C₂²	#41×C₃₈₉	1	4	yes	—
29	C₄	—	2	12	no	—
30	C₄	C₄²×C₃₈₉	1	4	yes	—
31	C₂	C₂×C₄²×C₃₈₉	1	1	yes	characteristic
32	C₂	#117×C₃₈₉	1	6	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.