Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
324 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 72 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. #10589686 | C2 | semidirect |
| 2. #10588710 | C2 | semidirect |
| 4. #10588376 | C2 | semidirect |
| 5. C9×Q8⋊C8 | C2 | semidirect |
| 6. #10588159 | C2 | semidirect |
| 7. #10588136 | C2 | semidirect |
| 105. Q8⋊C8 | D9 | semidirect |
| 234. C9 | #1628 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589686 | 2 |
| #10588710 | 2 |
| #10588527 | 2 |
| #10588376 | 2 |
| C9×Q8⋊C8 | 2 |
| #10588159 | 2 |
| #10588136 | 2 |
| #68245 | 3 |