Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
389 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 389 conjugacy classes of subgroups — too many to draw. Only its 78 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. #10590865 | C2 | semidirect |
| 3. #10590763 | C2 | semidirect |
| 4. C2×#63549 | C2 | semidirect |
| 5. C3×#4503 | C2 | semidirect |
| 6. C3×Dic3⋊C16 | C2 | semidirect |
| 7. #10589116 | C2 | semidirect |
| 35. #4503 | D3 | semidirect |
| 36. Dic3⋊C16 | D3 | semidirect |
| 290. C32 | #2210 | semidirect |
| 337. C3 | #69235 | semidirect |
| 338. C3 | #69288 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63626 | 2 |
| #10590865 | 2 |
| #10590763 | 2 |
| C2×#63549 | 2 |
| C3×#4503 | 2 |
| C3×Dic3⋊C16 | 2 |
| #10589116 | 2 |
| #69288 | 3 |
| #69235 | 3 |