Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
390 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 1. C32×#121 | C2 | semidirect |
| 2. C2×#3753 | C2 | semidirect |
| 3. #64139 | C2 | semidirect |
| 4. C2×#3748 | C2 | semidirect |
| 5. #63659 | C2 | semidirect |
| 6. #63636 | C2 | semidirect |
| 7. #63635 | C2 | semidirect |
| 22. C3×#121 | D3 | semidirect |
| 45. C3⋊(C3⋊C8) | D4 | semidirect |
| 78. #121 | C3⋊D3 | semidirect |
| 133. C32 | #469 | semidirect |
| 172. C3 | #5039 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#121 | 2 |
| C2×#3753 | 2 |
| #64139 | 2 |
| C2×#3748 | 2 |
| #63659 | 2 |
| #63636 | 2 |
| #63635 | 2 |
| #5039 | 3 |