Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
381 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 381 conjugacy classes of subgroups — too many to draw. Only its 118 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 |
|---|---|---|
| 4. C3×#4512 | C2 | semidirect |
| 5. #10589105 | C2 | semidirect |
| 12. #63625 | C4 | semidirect |
| 13. C16×C3⋊D3 | C4 | semidirect |
| 17. #63544 | C4 | semidirect |
| 18. #63542 | C4 | semidirect |
| 25. #4512 | D3 | semidirect |
| 40. C32×C16 | C2×C4 | semidirect |
| 41. C3⋊(C3⋊C16) | C2×C4 | semidirect |
| 42. C3×C3⋊C16 | C2×C4 | semidirect |
| 107. C3×C16 | C4×D3 | semidirect |
| 110. C3⋊C16 | C4×D3 | semidirect |
| 162. C3⋊D3 | #347 | semidirect |
| 178. C16 | #624 | semidirect |
| 197. C32 | C2×#347 | semidirect |
| 230. C3 | D3×#347 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3⋊D3×M32 | 2 |
| #10590668 | 2 |
| #10590625 | 2 |
| C3×#4512 | 2 |
| #10589105 | 2 |
| D3×#347 | 3 |