Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
156 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 44 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. D9×Q32 | C2 | semidirect |
| 3. C9×Q64 | C2 | semidirect |
| 4. #10588199 | C2 | semidirect |
| 5. #10588198 | C2 | semidirect |
| 6. #10588126 | C2 | semidirect |
| 7. #10588124 | C2 | semidirect |
| 64. Q64 | D9 | semidirect |
| 129. C9 | #2264 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10588599 | 2 |
| D9×Q32 | 2 |
| C9×Q64 | 2 |
| #10588199 | 2 |
| #10588198 | 2 |
| #10588126 | 2 |
| #10588124 | 2 |
| #69384 | 3 |