Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
690 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 186 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 |
|---|---|---|
| 1. #10589679 | C2 | semidirect |
| 2. C8×Q8×C9 | C2 | semidirect |
| 3. #10588527 | C2 | semidirect |
| 4. #10588377 | C2 | semidirect |
| 5. C4×D72 | C2 | semidirect |
| 50. Q8×C9 | D8 | semidirect |
| 61. C8×C9 | #41 | semidirect |
| 65. C8×Q8 | D9 | semidirect |
| 141. C9 | #3391 | semidirect |
| 143. Q8 | D72 | semidirect |
| 154. C8 | #3701 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589679 | 2 |
| C8×Q8×C9 | 2 |
| #10588527 | 2 |
| #10588377 | 2 |
| C4×D72 | 2 |
| #79910 | 3 |