Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
744 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 744 conjugacy classes of subgroups — too many to draw. Only its 192 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. #11723349 | C2 | semidirect |
| 3. #11722189 | C2 | semidirect |
| 4. C3×#63642 | C2 | semidirect |
| 5. #11722044 | C2 | semidirect |
| 13. C32×Dic12 | C4 | semidirect |
| 14. C32×D24 | C4 | semidirect |
| 15. C32×#204 | C4 | semidirect |
| 26. #63642 | D3 | semidirect |
| 58. C3×Dic12 | Dic3 | semidirect |
| 59. C3×D24 | Dic3 | semidirect |
| 60. C3×#204 | Dic3 | semidirect |
| 125. Dic12 | C3⋊Dic3 | semidirect |
| 126. D24 | C3⋊Dic3 | semidirect |
| 127. #204 | C3⋊Dic3 | semidirect |
| 150. C33 | #444 | semidirect |
| 209. C32 | #4717 | semidirect |
| 210. C32 | #5197 | semidirect |
| 236. C3 | #10590916 | semidirect |
| 237. C3 | #10592896 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#904 | 2 |
| #11723349 | 2 |
| #11722189 | 2 |
| C3×#63642 | 2 |
| #11722044 | 2 |
| #10592896 | 3 |
| #10590916 | 3 |