Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
522 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 126 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. C2×C32×C4⋊C4 | C2 | semidirect |
| 3. C2×C3×(C2×D3)⋊C4 | C2 | semidirect |
| 4. C2×C3×(C2×D3)⋊C4 | C2 | semidirect |
| 5. C3×C3⋊#95 | C2 | semidirect |
| 7. #4991 | C3 | direct (N × H) |
| 21. C2×C3×C4⋊C4 | D3 | semidirect |
| 22. C2×C3×C4⋊C4 | C2×C3 | semidirect |
| 25. C2×(C2×D3)⋊C4 | C2×C3 | semidirect |
| 26. C2×(C2×D3)⋊C4 | C2×C3 | semidirect |
| 28. C3⋊#95 | C2×C3 | semidirect |
| 43. C2×C32×C4 | D4 | semidirect |
| 90. C2×C4⋊C4 | C3×D3 | semidirect |
| 132. C2×C3×C4 | D12 | semidirect |
| 135. C2×C3×C4 | C3×D4 | semidirect |
| 196. C32 | #394 | semidirect |
| 214. C2×C4 | C3×D12 | semidirect |
| 250. C3 | #4991 | direct (N × H) |
| 251. C3 | C3×#394 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D12 | 2 |
| C2×C32×C4⋊C4 | 2 |
| C2×C3×(C2×D3)⋊C4 | 2 |
| C3×C3⋊#95 | 2 |
| C3×#394 | 3 |
| #4991 | 3 |