Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
473 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 473 conjugacy classes of subgroups — too many to draw. Only its 106 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×Q32 | C2 | semidirect |
| 4. C2×C3×#829 | C2 | semidirect |
| 5. C3×#4564 | C2 | semidirect |
| 7. C3×#4503 | C2 | semidirect |
| 9. #71502 | C3 | direct (N × H) |
| 29. C2×C3×Q32 | D3 | semidirect |
| 30. C2×C3×Q32 | C2×C3 | semidirect |
| 33. C2×#829 | C2×C3 | semidirect |
| 37. #4564 | C2×C3 | semidirect |
| 39. #4503 | C2×C3 | semidirect |
| 121. C2×Q32 | C3×D3 | semidirect |
| 185. C2×C3×D3 | Q32 | semidirect |
| 293. C2×D3 | C3×Q32 | semidirect |
| 312. C32 | #2188 | semidirect |
| 356. C3 | #71502 | direct (N × H) |
| 357. C3 | C3×#2188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D3×Q16 | 2 |
| C2×C32×Q32 | 2 |
| C3×#5188 | 2 |
| C2×C3×#829 | 2 |
| C3×#4564 | 2 |
| C3×(C2×D3)⋊C16 | 2 |
| C3×#4503 | 2 |
| C3×#2188 | 3 |
| #71502 | 3 |