Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
342 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 87 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. C4⋊C4×C3⋊D3 | C2 | semidirect |
| 3. C32×#102 | C2 | semidirect |
| 4. #63659 | C2 | semidirect |
| 5. #63647 | C2 | semidirect |
| 6. #63644 | C2 | semidirect |
| 7. #63635 | C2 | semidirect |
| 22. C3×#102 | D3 | semidirect |
| 72. #102 | C3⋊D3 | semidirect |
| 118. C32 | #481 | semidirect |
| 152. C3 | #4777 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64147 | 2 |
| C4⋊C4×C3⋊D3 | 2 |
| C32×#102 | 2 |
| #63659 | 2 |
| #63647 | 2 |
| #63644 | 2 |
| #63635 | 2 |
| #4777 | 3 |