Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
240 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 58 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. #63872 | C2 | semidirect |
| 3. #63642 | C2 | semidirect |
| 4. C3×#821 | C2 | semidirect |
| 5. #63562 | C2 | semidirect |
| 18. #821 | D3 | semidirect |
| 105. C32 | #490 | semidirect |
| 131. C3 | #4764 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #63914 | 2 |
| #63872 | 2 |
| #63642 | 2 |
| C3×#821 | 2 |
| #63562 | 2 |
| #4764 | 3 |