Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
546 conjugacy classes of subgroups; only the 222 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 222 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×Q16 | C2 | semidirect |
| 3. C2×C3×#216 | C2 | semidirect |
| 4. C3×D3×Q16 | C2 | direct (N × H) |
| 5. C2×C3×Dic12 | C2 | semidirect |
| 8. C2×D3×Q16 | C3 | direct (N × H) |
| 16. C32×Q16 | C22 | semidirect |
| 18. C3×#216 | C22 | semidirect |
| 20. C3×Dic12 | C22 | semidirect |
| 28. C2×C3×Q16 | D3 | direct (N × H) |
| 29. C2×C3×Q16 | C2×C3 | semidirect |
| 31. C2×#216 | C2×C3 | semidirect |
| 32. D3×Q16 | C2×C3 | direct (N × H) |
| 33. C2×Dic12 | C2×C3 | semidirect |
| 69. C3×Q16 | C2×D3 | direct (N × H) |
| 70. C3×Q16 | C22×C3 | semidirect |
| 76. #216 | C22×C3 | semidirect |
| 78. Dic12 | C22×C3 | semidirect |
| 81. C2×C3×D3 | Q16 | direct (N × H) |
| 92. C2×Q16 | C3×D3 | direct (N × H) |
| 129. C2×C32 | C2×Q16 | semidirect |
| 131. C3×D3 | C2×Q16 | direct (N × H) |
| 141. Q16 | C2×C3×D3 | direct (N × H) |
| 150. C2×D3 | C3×Q16 | direct (N × H) |
| 165. C32 | C22×Q16 | semidirect |
| 184. C2×C3 | D3×Q16 | direct (N × H) |
| 185. C2×C3 | C2×C3×Q16 | semidirect |
| 188. D3 | C2×C3×Q16 | direct (N × H) |
| 198. C3 | C2×D3×Q16 | direct (N × H) |
| 199. C3 | C22×C3×Q16 | semidirect |
| 201. C2 | C3×D3×Q16 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D3×Q8 | 2 |
| C2×C32×Q16 | 2 |
| C2×C3×#216 | 2 |
| C3×D3×Q16 | 2 |
| C2×C3×Dic12 | 2 |
| C2×C3×D3×C8 | 2 |
| C22×C3×Q16 | 3 |
| C2×D3×Q16 | 3 |