Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
156 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 3. C9×#107 | C2 | semidirect |
| 5. #63376 | C2 | semidirect |
| 6. #63368 | C2 | semidirect |
| 7. #63366 | C2 | semidirect |
| 67. #107 | D9 | semidirect |
| 111. C9 | #484 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #63459 | 2 |
| C4⋊C4×D9 | 2 |
| C9×#107 | 2 |
| (C2×D9)⋊C8 | 2 |
| #63376 | 2 |
| #63368 | 2 |
| #63366 | 2 |
| #4884 | 3 |