Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2340 conjugacy classes of subgroups; only the 585 normal subgroups are shown.
This group has 2340 conjugacy classes of subgroups — too many to draw. Only its 585 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×C32×#95 | C2 | semidirect |
| 3. C4×#3757 | C2 | semidirect |
| 4. #10592365 | C2 | semidirect |
| 5. C3⋊D3×#95 | C2 | semidirect |
| 6. #10592348 | C2 | semidirect |
| 7. #10592347 | C2 | semidirect |
| 13. C4×#638 | C4 | semidirect |
| 23. C2×C3×#95 | D3 | semidirect |
| 32. C22×C32×C4 | C2×C4 | semidirect |
| 40. C2×C4×C3⋊D3 | C2×C4 | semidirect |
| 41. #3757 | C2×C4 | semidirect |
| 42. #3752 | C2×C4 | semidirect |
| 43. #3750 | C2×C4 | semidirect |
| 45. C4×C3⋊Dic3 | C2×C4 | semidirect |
| 72. #638 | C42 | semidirect |
| 86. C2×#95 | C3⋊D3 | semidirect |
| 90. C22×C3×C4 | C4×D3 | semidirect |
| 165. C22×C4 | C4×C3⋊D3 | semidirect |
| 187. C32 | #2275 | semidirect |
| 227. C3 | #73322 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#638 | 2 |
| C2×C32×#95 | 2 |
| C4×#3757 | 2 |
| #10592365 | 2 |
| C3⋊D3×#95 | 2 |
| #10592348 | 2 |
| #10592347 | 2 |
| #73322 | 3 |