Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1148 conjugacy classes of subgroups; only the 330 normal subgroups are shown.
This group has 1148 conjugacy classes of subgroups — too many to draw. Only its 330 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×C32×D24 | C2 | semidirect |
| 2. C32×#874 | C2 | semidirect |
| 3. C33×C4×C8 | C2 | semidirect |
| 5. C3×#4695 | C3 | direct (N × H) |
| 13. C2×C3×D24 | C2×C3 | semidirect |
| 14. C3×#874 | C2×C3 | semidirect |
| 16. C32×C4×C8 | D3 | semidirect |
| 17. C32×C4×C8 | C2×C3 | semidirect |
| 23. C33×C8 | D4 | semidirect |
| 25. #4695 | C32 | direct (N × H) |
| 41. C33×C4 | D8 | semidirect |
| 45. C2×D24 | C2×C32 | semidirect |
| 46. #874 | C2×C32 | semidirect |
| 48. C3×C4×C8 | C3×D3 | semidirect |
| 49. C3×C4×C8 | C2×C32 | semidirect |
| 63. C32×C8 | D12 | semidirect |
| 64. C32×C8 | C3×D4 | semidirect |
| 90. C32×C4 | D24 | semidirect |
| 91. C32×C4 | C3×D8 | semidirect |
| 96. C4×C8 | C32×D3 | semidirect |
| 97. C33 | #493 | semidirect |
| 111. C3×C8 | C3×D12 | semidirect |
| 112. C3×C8 | C32×D4 | semidirect |
| 135. C3×C4 | C3×D24 | semidirect |
| 136. C3×C4 | C32×D8 | semidirect |
| 140. C32 | #4695 | direct (N × H) |
| 141. C32 | C3×#493 | semidirect |
| 147. C8 | C32×D12 | semidirect |
| 159. C4 | C32×D24 | semidirect |
| 162. C3 | C3×#4695 | direct (N × H) |
| 163. C3 | C32×#493 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×D24 | 2 |
| C32×#874 | 2 |
| C33×C4×C8 | 2 |
| C32×#493 | 3 |
| C3×#4695 | 3 |