Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
509 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 509 conjugacy classes of subgroups — too many to draw. Only its 98 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. C2×#63625 | C2 | semidirect |
| 3. #10590687 | C2 | semidirect |
| 4. C3×#4509 | C2 | semidirect |
| 5. C3×#4503 | C2 | semidirect |
| 6. #10589117 | C2 | semidirect |
| 7. #10589114 | C2 | semidirect |
| 17. #63810 | C4 | semidirect |
| 35. #4509 | D3 | semidirect |
| 36. #4503 | D3 | semidirect |
| 54. C3×Dic12 | C2×C4 | semidirect |
| 56. C3×D24 | C2×C4 | semidirect |
| 156. Dic12 | C4×D3 | semidirect |
| 158. D24 | C4×D3 | semidirect |
| 304. C32 | #2139 | semidirect |
| 352. C3 | #69189 | semidirect |
| 353. C3 | #69221 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63810 | 2 |
| C2×#63625 | 2 |
| #10590687 | 2 |
| C3×#4509 | 2 |
| C3×#4503 | 2 |
| #10589117 | 2 |
| #10589114 | 2 |
| #69221 | 3 |
| #69189 | 3 |