Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
337 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 337 conjugacy classes of subgroups — too many to draw. Only its 86 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. C2×C3×D3×C8 | C2 | semidirect |
| 3. #63841 | C2 | semidirect |
| 4. #63643 | C2 | semidirect |
| 5. C3×#821 | C2 | semidirect |
| 6. #63567 | C2 | semidirect |
| 7. #63563 | C2 | semidirect |
| 16. #3795 | C4 | semidirect |
| 28. C2×D3×C8 | D3 | semidirect |
| 33. #821 | D3 | semidirect |
| 198. C32 | #416 | semidirect |
| 243. C3 | #4772 | semidirect |
| 244. C3 | #5113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3795 | 2 |
| C2×C3×D3×C8 | 2 |
| #63841 | 2 |
| #63643 | 2 |
| C3×#821 | 2 |
| #63567 | 2 |
| #63563 | 2 |
| #5113 | 3 |
| #4772 | 3 |