Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
595 conjugacy classes of subgroups; only the 246 normal subgroups are shown.
This group has 595 conjugacy classes of subgroups — too many to draw. Only its 246 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 |
|---|---|---|
| 1. C2×C3×D3×Q8 | C2 | semidirect |
| 2. C32×C4×Q8 | C2 | semidirect |
| 3. C3×#897 | C2 | semidirect |
| 5. C3×#869 | C2 | semidirect |
| 7. Q8×D12 | C3 | direct (N × H) |
| 19. C2×D3×Q8 | C2×C3 | semidirect |
| 23. C3×C4×Q8 | D3 | semidirect |
| 24. C3×C4×Q8 | C2×C3 | semidirect |
| 26. #897 | C2×C3 | semidirect |
| 28. #869 | C2×C3 | semidirect |
| 30. C32×Q8 | D4 | semidirect |
| 35. C3×D12 | Q8 | direct (N × H) |
| 65. C2×C3×D3 | C2×Q8 | semidirect |
| 68. C32×C4 | C2×Q8 | semidirect |
| 73. C4×Q8 | C3×D3 | semidirect |
| 79. C3×Q8 | D12 | direct (N × H) |
| 80. C3×Q8 | C3×D4 | semidirect |
| 94. D12 | C3×Q8 | direct (N × H) |
| 119. C2×D3 | C2×C3×Q8 | semidirect |
| 127. C3×C4 | D3×Q8 | semidirect |
| 129. C3×C4 | C2×C3×Q8 | semidirect |
| 131. C32 | D4×Q8 | semidirect |
| 134. Q8 | C3×D12 | direct (N × H) |
| 159. C4 | C3×D3×Q8 | semidirect |
| 161. C3 | Q8×D12 | direct (N × H) |
| 162. C3 | C3×D4×Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D3×Q8 | 2 |
| C32×C4×Q8 | 2 |
| C3×#897 | 2 |
| C3×C4×D12 | 2 |
| C3×#869 | 2 |
| C3×D4×Q8 | 3 |
| Q8×D12 | 3 |