Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
684 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 221 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 |
|---|---|---|
| 6. C32×C4⋊Q8 | C4 | semidirect |
| 7. C32×C4⋊Q8 | C4 | semidirect |
| 12. C32×C4×Q8 | C4 | semidirect |
| 46. C3×C4⋊Q8 | Dic3 | semidirect |
| 47. C3×C4⋊Q8 | Dic3 | semidirect |
| 52. C3×C4×Q8 | Dic3 | semidirect |
| 116. C4⋊Q8 | C3⋊Dic3 | semidirect |
| 117. C4⋊Q8 | C3⋊Dic3 | semidirect |
| 122. C4×Q8 | C3⋊Dic3 | semidirect |
| 186. C32 | #1506 | semidirect |
| 222. C3 | #71836 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#533 | 2 |
| #10592631 | 2 |
| #10592625 | 2 |
| #10589404 | 2 |
| #71836 | 3 |