Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
760 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 164 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. C3×#64078 | C2 | semidirect |
| 3. #11722173 | C2 | semidirect |
| 4. #11722037 | C2 | semidirect |
| 18. #64078 | D3 | semidirect |
| 156. C33 | #489 | semidirect |
| 224. C32 | #5055 | semidirect |
| 225. C32 | #5089 | semidirect |
| 257. C3 | #10590280 | semidirect |
| 258. C3 | #10592754 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64078 | 2 |
| C32×#875 | 2 |
| #11722173 | 2 |
| #11722037 | 2 |
| #11722031 | 2 |
| #10592754 | 3 |
| #10590280 | 3 |