Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
261 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 261 conjugacy classes of subgroups — too many to draw. Only its 72 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. #10590871 | C2 | semidirect |
| 3. #10589379 | C2 | semidirect |
| 5. C3×#4511 | C2 | semidirect |
| 6. #10589136 | C2 | semidirect |
| 34. #4511 | D3 | semidirect |
| 223. C32 | #2231 | semidirect |
| 254. C3 | #69247 | semidirect |
| 255. C3 | #69308 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10590915 | 2 |
| #10590871 | 2 |
| #10589379 | 2 |
| C3×#4518 | 2 |
| C3×#4511 | 2 |
| #10589136 | 2 |
| #10589124 | 2 |
| #69308 | 3 |
| #69247 | 3 |