Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1773 conjugacy classes of subgroups; only the 258 normal subgroups are shown.
This group has 1773 conjugacy classes of subgroups — too many to draw. Only its 258 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, socle, cosocle | C23×C32 | C24 |
| Fitting | C32×#95 | C22 |
| hypercenter | #95 | D32 |
| hypocenter | C32 | #2397 |
| LCS | G ▷ C23×C32 ▷ C32 | |
| UCS | C1 ◁ C23 ◁ #95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×Dic3×D12 | C2 | semidirect |
| 2. C2×#63880 | C2 | semidirect |
| 3. #10592376 | C2 | semidirect |
| 4. C3×#4671 | C2 | semidirect |
| 5. C3×#4648 | C2 | semidirect |
| 6. #10591391 | C2 | semidirect |
| 7. #10591317 | C2 | semidirect |
| 37. #4671 | D3 | semidirect |
| 38. #4648 | D3 | semidirect |
| 57. C3×C4×Dic3 | D4 | semidirect |
| 167. C4×Dic3 | D12 | semidirect |
| 316. C32 | #2397 | semidirect |
| 370. C3 | #73418 | semidirect |
| 371. C3 | #76667 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic3×D12 | 2 |
| C2×#63880 | 2 |
| #10592376 | 2 |
| C3×#4671 | 2 |
| C3×#4648 | 2 |
| #10591391 | 2 |
| #10591317 | 2 |
| #76667 | 3 |
| #73418 | 3 |