Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
1014 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 1014 conjugacy classes of subgroups — too many to draw. Only its 271 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×#117 | C2 | semidirect |
| 3. #64135 | C2 | semidirect |
| 4. #64102 | C2 | semidirect |
| 5. C22⋊C4×C3⋊D3 | C2 | semidirect |
| 6. C4×C4⋊(C3⋊D3) | C2 | semidirect |
| 10. C2×C4⋊(C3⋊D3) | C4 | semidirect |
| 13. C2×C4×C3⋊D3 | C22 | semidirect |
| 14. C32×C4⋊C4 | C22 | semidirect |
| 16. C32×C42 | C22 | semidirect |
| 18. #3752 | C22 | semidirect |
| 19. C4⋊(C3⋊Dic3) | C22 | semidirect |
| 20. C4×C3⋊Dic3 | C22 | semidirect |
| 22. C3×#117 | D3 | semidirect |
| 29. C22×C3⋊D3 | C2×C4 | semidirect |
| 31. C2×C32×C4 | C2×C4 | semidirect |
| 36. C4⋊(C3⋊D3) | C2×C4 | semidirect |
| 37. C4⋊(C3⋊D3) | C2×C4 | semidirect |
| 46. C3×C4⋊C4 | C2×D3 | semidirect |
| 48. C3×C42 | C2×D3 | semidirect |
| 67. #117 | C3⋊D3 | semidirect |
| 73. C2×C3×C4 | C4×D3 | semidirect |
| 92. C4⋊C4 | C2×C3⋊D3 | semidirect |
| 97. C42 | C2×C3⋊D3 | semidirect |
| 108. C32 | #518 | semidirect |
| 117. C2×C4 | C4×C3⋊D3 | semidirect |
| 135. C3 | #5521 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊(C3⋊D3) | 2 |
| C32×#117 | 2 |
| #64135 | 2 |
| #64102 | 2 |
| C22⋊C4×C3⋊D3 | 2 |
| C4×C4⋊(C3⋊D3) | 2 |
| #5521 | 3 |