Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
397 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 397 conjugacy classes of subgroups — too many to draw. Only its 134 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. C3×Dic3×D8 | C2 | semidirect |
| 3. C3×#4562 | C2 | semidirect |
| 4. C3×#4504 | C2 | semidirect |
| 5. C3×Dic3×C16 | C2 | semidirect |
| 7. Dic3×D16 | C3 | direct (N × H) |
| 10. C32×D16 | C4 | semidirect |
| 20. Dic3×D8 | C2×C3 | semidirect |
| 24. #4562 | C2×C3 | semidirect |
| 25. #4504 | C2×C3 | semidirect |
| 26. Dic3×C16 | C2×C3 | semidirect |
| 30. C32×D8 | C2×C4 | semidirect |
| 36. C32×C16 | C2×C4 | semidirect |
| 45. C3×D16 | Dic3 | direct (N × H) |
| 46. C3×D16 | C3×C4 | semidirect |
| 83. C3×D8 | C2×Dic3 | semidirect |
| 84. C3×D8 | C2×C3×C4 | semidirect |
| 98. C3×C16 | C2×Dic3 | semidirect |
| 99. C3×C16 | C2×C3×C4 | semidirect |
| 109. C3×Dic3 | D16 | direct (N × H) |
| 112. D16 | C3×Dic3 | direct (N × H) |
| 153. D8 | C2×C3×Dic3 | semidirect |
| 160. C16 | C2×C3×Dic3 | semidirect |
| 184. Dic3 | C3×D16 | direct (N × H) |
| 185. C32 | C4×D16 | semidirect |
| 219. C3 | Dic3×D16 | direct (N × H) |
| 220. C3 | C3×C4×D16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×D16 | 2 |
| C3×Dic3×D8 | 2 |
| C3×#4562 | 2 |
| C3×#4504 | 2 |
| C3×Dic3×C16 | 2 |
| C3×C4×D16 | 3 |
| Dic3×D16 | 3 |