Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
239 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 239 conjugacy classes of subgroups — too many to draw. Only its 106 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. C32×C4⋊C8 | C2 | semidirect |
| 4. C3×#815 | C2 | semidirect |
| 5. C3×C4⋊(C3⋊C8) | C2 | semidirect |
| 7. #4835 | C3 | direct (N × H) |
| 21. C3×C4⋊C8 | D3 | semidirect |
| 22. C3×C4⋊C8 | C2×C3 | semidirect |
| 26. #815 | C2×C3 | semidirect |
| 27. C4⋊(C3⋊C8) | C2×C3 | semidirect |
| 75. C4⋊C8 | C3×D3 | semidirect |
| 148. C32 | #432 | semidirect |
| 185. C3 | #4835 | direct (N × H) |
| 186. C3 | C3×#432 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C42×D3 | 2 |
| C32×C4⋊C8 | 2 |
| C3×(C2×D3)⋊C8 | 2 |
| C3×#815 | 2 |
| C3×C4⋊(C3⋊C8) | 2 |
| C3×#432 | 3 |
| #4835 | 3 |