Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
141 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 141 conjugacy classes of subgroups — too many to draw. Only its 33 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. #63393 | C2 | semidirect |
| 3. #63391 | C2 | semidirect |
| 5. C24×C9 | C4 | semidirect |
| 9. C9×C22⋊C4 | C4 | semidirect |
| 66. C24 | Dic9 | semidirect |
| 72. C22⋊C4 | Dic9 | 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 |
|---|---|
| C9×#120 | 2 |
| #63393 | 2 |
| #63391 | 2 |
| #4536 | 3 |