Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
323 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 323 conjugacy classes of subgroups — too many to draw. Only its 78 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. C3×D3×M16 | C2 | semidirect |
| 3. D3×#208 | C2 | semidirect |
| 4. #63650 | C2 | semidirect |
| 5. C3×#824 | C2 | semidirect |
| 6. #63560 | C2 | semidirect |
| 7. #63559 | C2 | semidirect |
| 32. D3×M16 | D3 | semidirect |
| 36. #824 | D3 | semidirect |
| 216. C32 | #413 | semidirect |
| 263. C3 | #4751 | semidirect |
| 264. C3 | #5132 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3799 | 2 |
| C3×D3×M16 | 2 |
| D3×#208 | 2 |
| #63650 | 2 |
| C3×#824 | 2 |
| #63560 | 2 |
| #63559 | 2 |
| #5132 | 3 |
| #4751 | 3 |