Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1296 conjugacy classes of subgroups; only the 305 normal subgroups are shown.
This group has 1296 conjugacy classes of subgroups — too many to draw. Only its 305 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×#376 | C2 | semidirect |
| 3. C4×#3750 | C2 | semidirect |
| 6. #10592361 | C2 | semidirect |
| 7. #10592357 | C2 | semidirect |
| 22. C3×#376 | D3 | semidirect |
| 82. #376 | C3⋊D3 | semidirect |
| 171. C32 | #2401 | semidirect |
| 207. C3 | #73420 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#376 | 2 |
| C4×#3752 | 2 |
| C4×#3750 | 2 |
| #10592375 | 2 |
| #10592374 | 2 |
| #10592361 | 2 |
| #10592357 | 2 |
| #73420 | 3 |