Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
179 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 179 conjugacy classes of subgroups — too many to draw. Only its 49 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 |
|---|---|---|
| 15. #3395 | C9 | semidirect |
| 29. Q8⋊C9 | Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #557⋊C9 | 2 |
| C8×Q8⋊C9 | 2 |
| C3×#3395 | 3 |
| C9×#107 | 4 |