Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
141 conjugacy classes of subgroups; only the 29 normal subgroups are shown.
This group has 141 conjugacy classes of subgroups — too many to draw. Only its 29 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×#99 | C2 | semidirect |
| 3. #63391 | C2 | semidirect |
| 5. C23×D9 | C4 | semidirect |
| 9. #3676 | C4 | semidirect |
| 49. #99 | D9 | semidirect |
| 86. C9 | AΣL(1,𝔽16) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #63499 | 2 |
| C9×#99 | 2 |
| #63391 | 2 |
| #4471 | 3 |