Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1841 conjugacy classes of subgroups; only the 254 normal subgroups are shown.
This group has 1841 conjugacy classes of subgroups — too many to draw. Only its 254 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×#63894 | C2 | semidirect |
| 2. C2×#63880 | C2 | semidirect |
| 3. #10592370 | C2 | semidirect |
| 4. C3×#4677 | C2 | semidirect |
| 5. C3×#4648 | C2 | semidirect |
| 6. #10591395 | C2 | semidirect |
| 7. #10591350 | C2 | semidirect |
| 33. #4677 | D3 | semidirect |
| 38. #4648 | D3 | semidirect |
| 57. C3×C4×Dic3 | D4 | semidirect |
| 168. C4×Dic3 | D12 | semidirect |
| 321. C32 | #2397 | semidirect |
| 375. C3 | #73418 | semidirect |
| 376. C3 | #78019 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63894 | 2 |
| C2×#63880 | 2 |
| #10592370 | 2 |
| C3×#4677 | 2 |
| C3×#4648 | 2 |
| #10591395 | 2 |
| #10591350 | 2 |
| #78019 | 3 |
| #73418 | 3 |