Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
993 conjugacy classes of subgroups; only the 244 normal subgroups are shown.
This group has 993 conjugacy classes of subgroups — too many to draw. Only its 244 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D32 |
| commutator | C22×C32 | C23×C4 |
| Fitting | C2×C32×C42 | C22 |
| socle, prime radical, cosocle | C23×C32 | C24 |
| hypercenter | C2×C42 | D32 |
| hypocenter | C32 | #2381 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C23 ◁ C2×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 9. #64078 | C4 | semidirect |
| 164. C32 | #2381 | semidirect |
| 192. C3 | #74265 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64078 | 2 |
| C3×#4937 | 2 |
| #10591273 | 2 |
| #10591271 | 2 |
| #74265 | 3 |