Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
317 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 317 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. #10590714 | C2 | semidirect |
| 3. #10589373 | C2 | semidirect |
| 4. C3×#4509 | C2 | semidirect |
| 5. C3×#4504 | C2 | semidirect |
| 6. #10589142 | C2 | semidirect |
| 7. #10589114 | C2 | semidirect |
| 28. #4509 | D3 | semidirect |
| 32. #4504 | D3 | semidirect |
| 259. C32 | #2234 | semidirect |
| 303. C3 | #69201 | semidirect |
| 304. C3 | #69323 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10590844 | 2 |
| #10590714 | 2 |
| #10589373 | 2 |
| C3×#4509 | 2 |
| C3×#4504 | 2 |
| #10589142 | 2 |
| #10589114 | 2 |
| #69323 | 3 |
| #69201 | 3 |