Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
258 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
| 3. #10588702 | C2 | semidirect |
| 6. #10588159 | C2 | semidirect |
| 7. #10588134 | C2 | semidirect |
| 68. Q8×C9 | SD16 | semidirect |
| 84. C8×C9 | SD16 | semidirect |
| 90. C8×Q8 | D9 | semidirect |
| 196. C9 | #1666 | semidirect |
| 201. Q8 | #3664 | semidirect |
| 217. C8 | #3675 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×Q8×C9 | 2 |
| #10588710 | 2 |
| #10588702 | 2 |
| #10588375 | 2 |
| #10588163 | 2 |
| #10588159 | 2 |
| #10588134 | 2 |
| #70938 | 3 |