Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
334 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 72 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×#3756 | C2 | semidirect |
| 3. #63857 | C2 | semidirect |
| 4. C2×#3716 | C2 | semidirect |
| 5. C3×#835 | C2 | semidirect |
| 6. #63562 | C2 | semidirect |
| 7. (C2×D3)⋊(C3⋊C8) | C2 | semidirect |
| 35. #835 | D3 | semidirect |
| 211. C32 | #452 | semidirect |
| 258. C3 | #4808 | semidirect |
| 259. C3 | #5239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#239 | 2 |
| C2×#3756 | 2 |
| #63857 | 2 |
| C2×#3716 | 2 |
| C3×#835 | 2 |
| #63562 | 2 |
| (C2×D3)⋊(C3⋊C8) | 2 |
| #5239 | 3 |
| #4808 | 3 |