Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
406 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 2. C3×#5070 | C2 | semidirect |
| 3. #10590363 | C2 | semidirect |
| 4. C3⋊C8×D12 | C2 | semidirect |
| 5. #10589410 | C2 | semidirect |
| 6. #10589099 | C2 | semidirect |
| 7. #10589093 | C2 | semidirect |
| 29. #5070 | D3 | semidirect |
| 314. C32 | #1681 | semidirect |
| 367. C3 | #71007 | semidirect |
| 368. C3 | #71201 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5072 | 2 |
| C3×#5070 | 2 |
| #10590363 | 2 |
| C3⋊C8×D12 | 2 |
| #10589410 | 2 |
| #10589099 | 2 |
| #10589093 | 2 |
| #71201 | 3 |
| #71007 | 3 |