Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
402 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 113 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×#430 | C2 | semidirect |
| 3. #10589419 | C2 | semidirect |
| 4. #10589361 | C2 | semidirect |
| 5. #10589360 | C2 | semidirect |
| 16. C3×#430 | D3 | semidirect |
| 58. #430 | C3⋊D3 | semidirect |
| 134. C32 | #2238 | semidirect |
| 162. C3 | #70723 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#430 | 2 |
| #10592834 | 2 |
| #10589419 | 2 |
| #10589361 | 2 |
| #10589360 | 2 |
| #70723 | 3 |