Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
786 conjugacy classes of subgroups; only the 246 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 246 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. C9×#376 | C2 | semidirect |
| 4. C4×Dic9⋊C4 | C2 | semidirect |
| 5. C42×Dic9 | C2 | semidirect |
| 7. #10588332 | C2 | semidirect |
| 19. #63434 | C4 | semidirect |
| 87. #376 | D9 | semidirect |
| 186. C9 | #2298 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63434 | 2 |
| C9×#376 | 2 |
| C4×(C2×D9)⋊C4 | 2 |
| C4×Dic9⋊C4 | 2 |
| C42×Dic9 | 2 |
| #10588349 | 2 |
| #10588332 | 2 |
| #73385 | 3 |