Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
189 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 189 conjugacy classes of subgroups — too many to draw. Only its 68 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. #10588360 | C2 | semidirect |
| 4. #10588171 | C2 | semidirect |
| 5. #10588140 | C2 | semidirect |
| 23. C9×Q16 | Q8 | semidirect |
| 25. C9×D8 | Q8 | semidirect |
| 111. Q16 | Dic18 | semidirect |
| 113. D8 | Dic18 | semidirect |
| 130. C9 | #2230 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#443 | 2 |
| #10588360 | 2 |
| #10588243 | 2 |
| #10588171 | 2 |
| #10588140 | 2 |
| #70919 | 3 |