Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
884 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 884 conjugacy classes of subgroups — too many to draw. Only its 234 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. C33×#125 | C2 | semidirect |
| 3. C32×#809 | C2 | semidirect |
| 4. C32×#803 | C2 | semidirect |
| 6. C3×#5067 | C3 | direct (N × H) |
| 15. C32×#125 | D3 | semidirect |
| 16. C32×#125 | C2×C3 | semidirect |
| 20. C3×#809 | C2×C3 | semidirect |
| 21. C3×#803 | C2×C3 | semidirect |
| 30. #5067 | C32 | direct (N × H) |
| 54. C3×#125 | C3×D3 | semidirect |
| 55. C3×#125 | C2×C32 | semidirect |
| 59. #809 | C2×C32 | semidirect |
| 60. #803 | C2×C32 | semidirect |
| 114. #125 | C32×D3 | semidirect |
| 117. C33 | #490 | semidirect |
| 166. C32 | #5067 | direct (N × H) |
| 167. C32 | C3×#490 | semidirect |
| 190. C3 | C3×#5067 | direct (N × H) |
| 191. C3 | C32×#490 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#125 | 2 |
| C32×#874 | 2 |
| C32×#809 | 2 |
| C32×#803 | 2 |
| C32×#490 | 3 |
| C3×#5067 | 3 |