Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
784 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 158 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. #11723354 | C2 | semidirect |
| 3. #11722185 | C2 | semidirect |
| 4. C32×#819 | C2 | semidirect |
| 5. #11722045 | C2 | semidirect |
| 12. C3×#3746 | C4 | semidirect |
| 13. C3×#3745 | C4 | semidirect |
| 14. C3×#3744 | C4 | semidirect |
| 27. C3×#819 | D3 | semidirect |
| 53. #3746 | Dic3 | semidirect |
| 54. #3745 | Dic3 | semidirect |
| 55. #3744 | Dic3 | semidirect |
| 77. #819 | C3⋊D3 | semidirect |
| 154. C33 | #444 | semidirect |
| 215. C32 | #4894 | semidirect |
| 216. C32 | #5197 | semidirect |
| 242. C3 | #10590920 | semidirect |
| 243. C3 | #10592593 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64113 | 2 |
| #11723354 | 2 |
| #11722185 | 2 |
| C32×#819 | 2 |
| #11722045 | 2 |
| #10592593 | 3 |
| #10590920 | 3 |