Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
246 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 246 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×C4⋊C4 | C2 | semidirect |
| 3. C32×#106 | C2 | semidirect |
| 4. C3×#821 | C2 | semidirect |
| 5. C3×(C2×D3)⋊C8 | C2 | semidirect |
| 6. C3×#809 | C2 | semidirect |
| 7. C3×#808 | C2 | semidirect |
| 9. #4863 | C3 | direct (N × H) |
| 24. D3×C4⋊C4 | C2×C3 | semidirect |
| 27. C3×#106 | D3 | semidirect |
| 28. C3×#106 | C2×C3 | semidirect |
| 32. #821 | C2×C3 | semidirect |
| 33. (C2×D3)⋊C8 | C2×C3 | semidirect |
| 34. #809 | C2×C3 | semidirect |
| 35. #808 | C2×C3 | semidirect |
| 93. #106 | C3×D3 | semidirect |
| 178. C32 | #481 | semidirect |
| 221. C3 | #4863 | direct (N × H) |
| 222. C3 | C3×#481 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#895 | 2 |
| C3×D3×C4⋊C4 | 2 |
| C32×#106 | 2 |
| C3×#821 | 2 |
| C3×(C2×D3)⋊C8 | 2 |
| C3×#809 | 2 |
| C3×#808 | 2 |
| C3×#481 | 3 |
| #4863 | 3 |