Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
426 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 151 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 |
|---|---|---|
| 3. #10592883 | C2 | semidirect |
| 5. #10589431 | C2 | semidirect |
| 6. #10589379 | C2 | semidirect |
| 7. #10589378 | C2 | semidirect |
| 13. C32×Q32 | C4 | semidirect |
| 14. C32×SD32 | C4 | semidirect |
| 52. C3×Q32 | Dic3 | semidirect |
| 53. C3×SD32 | Dic3 | semidirect |
| 112. Q32 | C3⋊Dic3 | semidirect |
| 113. SD32 | C3⋊Dic3 | semidirect |
| 164. C32 | #2180 | semidirect |
| 190. C3 | #71521 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#510 | 2 |
| #10592896 | 2 |
| #10592883 | 2 |
| #10589432 | 2 |
| #10589431 | 2 |
| #10589379 | 2 |
| #10589378 | 2 |
| #71521 | 3 |