Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
345 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 345 conjugacy classes of subgroups — too many to draw. Only its 80 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. C2×C9×#135 | C2 | semidirect |
| 2. C2×#63387 | C2 | semidirect |
| 3. C2×#63385 | C2 | semidirect |
| 4. #10588796 | C2 | semidirect |
| 5. #10588241 | C2 | semidirect |
| 6. #10588239 | C2 | semidirect |
| 7. #10588226 | C2 | semidirect |
| 41. C9×Q16 | D4 | semidirect |
| 44. C9×D8 | D4 | semidirect |
| 92. C2×#135 | D9 | semidirect |
| 190. Q16 | #611 | semidirect |
| 195. D8 | #611 | semidirect |
| 219. C9 | #2186 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×#135 | 2 |
| C2×#63387 | 2 |
| C2×#63385 | 2 |
| #10588796 | 2 |
| #10588241 | 2 |
| #10588239 | 2 |
| #10588226 | 2 |
| #72082 | 3 |