Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
449 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 449 conjugacy classes of subgroups — too many to draw. Only its 96 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×#4679 | C2 | semidirect |
| 3. #10590367 | C2 | semidirect |
| 4. C3×#4457 | C2 | semidirect |
| 5. #10589091 | C2 | semidirect |
| 25. #4679 | D3 | semidirect |
| 29. #4457 | D3 | semidirect |
| 85. C32×C8 | SD16 | semidirect |
| 191. C3×C8 | #204 | semidirect |
| 192. C3×C8 | #215 | semidirect |
| 242. C32 | #1688 | semidirect |
| 258. C8 | #3717 | semidirect |
| 282. C3 | #68550 | semidirect |
| 283. C3 | #70959 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592394 | 2 |
| C3×#4679 | 2 |
| #10590367 | 2 |
| C3×#4457 | 2 |
| #10589091 | 2 |
| #70959 | 3 |
| #68550 | 3 |