Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
240 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 66 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. #10588554 | C2 | semidirect |
| 3. C9×#357 | C2 | semidirect |
| 4. #10588239 | C2 | semidirect |
| 5. #10588186 | C2 | semidirect |
| 6. C16×Dic9 | C2 | semidirect |
| 7. #10588168 | C2 | semidirect |
| 79. #357 | D9 | semidirect |
| 176. C9 | #2240 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10588831 | 2 |
| #10588554 | 2 |
| C9×#357 | 2 |
| #10588239 | 2 |
| #10588186 | 2 |
| C16×Dic9 | 2 |
| #10588168 | 2 |
| #69183 | 3 |