Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
429 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 429 conjugacy classes of subgroups — too many to draw. Only its 102 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×C3×D3×C8 | C2 | semidirect |
| 3. D3×C4⋊Dic3 | C2 | semidirect |
| 4. #63648 | C2 | semidirect |
| 5. C3×#821 | C2 | semidirect |
| 6. #63564 | C2 | semidirect |
| 7. #63563 | C2 | semidirect |
| 17. D3×D12 | C4 | semidirect |
| 18. C2×C32×C8 | C22 | semidirect |
| 19. C4⋊(C3⋊Dic3) | C22 | semidirect |
| 20. C3×C4⋊Dic3 | C22 | semidirect |
| 21. C2×C3×C3⋊C8 | C22 | semidirect |
| 28. C2×D3×C8 | D3 | semidirect |
| 37. #821 | D3 | direct (N × H) |
| 48. C4⋊(C3⋊D3) | C2×C4 | semidirect |
| 52. C3×D12 | C2×C4 | semidirect |
| 80. C2×C3×C8 | C2×D3 | semidirect |
| 81. C2×C3×C8 | C2×D3 | semidirect |
| 87. C4⋊Dic3 | C2×D3 | semidirect |
| 89. C2×C3⋊C8 | C2×D3 | semidirect |
| 151. D12 | C4×D3 | semidirect |
| 165. C3×D3 | #102 | semidirect |
| 176. C2×C8 | D32 | semidirect |
| 219. C32 | C2×#102 | semidirect |
| 255. D3 | #821 | direct (N × H) |
| 273. C3 | D3×#102 | semidirect |
| 274. C3 | C2×#821 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×D12 | 2 |
| C2×C3×D3×C8 | 2 |
| D3×C4⋊Dic3 | 2 |
| #63648 | 2 |
| C3×#821 | 2 |
| #63564 | 2 |
| #63563 | 2 |
| C2×#821 | 3 |
| D3×#102 | 3 |