Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
636 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 198 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. C9×#500 | C2 | semidirect |
| 3. #10588758 | C2 | semidirect |
| 5. #10588554 | C2 | semidirect |
| 7. #10588362 | C2 | semidirect |
| 52. C8×D9 | Q8 | semidirect |
| 86. C8×C9 | C2×Q8 | semidirect |
| 87. C9⋊C8 | C2×Q8 | semidirect |
| 92. #500 | D9 | direct (N × H) |
| 165. D9 | #500 | direct (N × H) |
| 199. C9 | C2×#500 | semidirect |
| 217. C8 | Q8×D9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D9×C4⋊Q8 | 2 |
| C9×#500 | 2 |
| #10588758 | 2 |
| D9×#107 | 2 |
| #10588554 | 2 |
| C4×C8×D9 | 2 |
| #10588362 | 2 |
| D3×#500 | 3 |