Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1028 conjugacy classes of subgroups; only the 330 normal subgroups are shown.
This group has 1028 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×#204 | C2 | semidirect |
| 3. C32×#869 | C2 | semidirect |
| 4. C33×C4×C8 | C2 | semidirect |
| 6. C3×#4693 | C3 | direct (N × H) |
| 17. C2×C3×#204 | C2×C3 | semidirect |
| 19. C3×#869 | C2×C3 | semidirect |
| 21. C32×C4×C8 | D3 | semidirect |
| 22. C32×C4×C8 | C2×C3 | semidirect |
| 30. C33×C8 | D4 | semidirect |
| 32. #4693 | C32 | direct (N × H) |
| 52. C33×C4 | SD16 | semidirect |
| 58. C2×#204 | C2×C32 | semidirect |
| 60. #869 | C2×C32 | semidirect |
| 62. C3×C4×C8 | C3×D3 | semidirect |
| 63. C3×C4×C8 | C2×C32 | semidirect |
| 81. C32×C8 | D12 | semidirect |
| 82. C32×C8 | C3×D4 | semidirect |
| 113. C32×C4 | #204 | semidirect |
| 114. C32×C4 | C3×SD16 | semidirect |
| 121. C4×C8 | C32×D3 | semidirect |
| 122. C33 | #492 | semidirect |
| 140. C3×C8 | C3×D12 | semidirect |
| 141. C3×C8 | C32×D4 | semidirect |
| 167. C3×C4 | C3×#204 | semidirect |
| 168. C3×C4 | C32×SD16 | semidirect |
| 173. C32 | #4693 | direct (N × H) |
| 174. C32 | C3×#492 | semidirect |
| 182. C8 | C32×D12 | semidirect |
| 195. C4 | C32×#204 | semidirect |
| 198. C3 | C3×#4693 | direct (N × H) |
| 199. C3 | C32×#492 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#204 | 2 |
| C32×#874 | 2 |
| C32×#869 | 2 |
| C33×C4×C8 | 2 |
| C32×#492 | 3 |
| C3×#4693 | 3 |