Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
273 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 273 conjugacy classes of subgroups — too many to draw. Only its 68 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. #10588753 | C2 | semidirect |
| 3. #10588530 | C2 | semidirect |
| 4. #10588522 | C2 | semidirect |
| 5. C9×#331 | C2 | semidirect |
| 6. #10588159 | C2 | semidirect |
| 7. #10588156 | C2 | semidirect |
| 89. C9⋊C8 | D8 | semidirect |
| 96. #331 | D9 | semidirect |
| 208. C9 | #1685 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10588754 | 2 |
| #10588753 | 2 |
| #10588530 | 2 |
| #10588522 | 2 |
| C9×#331 | 2 |
| #10588159 | 2 |
| #10588156 | 2 |
| #68398 | 3 |