Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
784 conjugacy classes of subgroups; only the 190 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 190 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. #11723350 | C2 | semidirect |
| 3. #11722185 | C2 | semidirect |
| 4. C3×#63646 | C2 | semidirect |
| 5. #11722043 | C2 | semidirect |
| 13. C32×Dic12 | C4 | semidirect |
| 14. C32×D24 | C4 | semidirect |
| 15. C32×#204 | C4 | semidirect |
| 23. #63646 | D3 | semidirect |
| 59. C3×Dic12 | Dic3 | semidirect |
| 60. C3×D24 | Dic3 | semidirect |
| 61. C3×#204 | Dic3 | semidirect |
| 128. Dic12 | C3⋊Dic3 | semidirect |
| 129. D24 | C3⋊Dic3 | semidirect |
| 130. #204 | C3⋊Dic3 | semidirect |
| 154. C33 | #444 | semidirect |
| 215. C32 | #4894 | semidirect |
| 216. C32 | #5197 | semidirect |
| 242. C3 | #10590920 | semidirect |
| 243. 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 |
| #11723350 | 2 |
| #11722185 | 2 |
| C3×#63646 | 2 |
| #11722043 | 2 |
| #10592896 | 3 |
| #10590920 | 3 |