Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
249 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 249 conjugacy classes of subgroups — too many to draw. Only its 88 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. C8×Q8×C9 | C2 | semidirect |
| 4. #10588212 | C2 | semidirect |
| 6. #10588156 | C2 | semidirect |
| 7. #10588131 | C2 | semidirect |
| 67. Q8×C9 | M16 | semidirect |
| 85. C8×Q8 | D9 | semidirect |
| 191. C9 | #1588 | semidirect |
| 194. Q8 | #3663 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×Q8×C9 | 2 |
| C4×#3675 | 2 |
| #10588370 | 2 |
| #10588212 | 2 |
| #10588162 | 2 |
| #10588156 | 2 |
| #10588131 | 2 |
| #70936 | 3 |