Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
414 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 66 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×#64228 | C2 | semidirect |
| 3. C3×#64222 | C2 | semidirect |
| 5. C3×#63802 | C2 | semidirect |
| 7. C3×#63767 | C2 | semidirect |
| 8. #10593291 | C3 | direct (N × H) |
| 24. #64228 | C2×C3 | semidirect |
| 26. #64222 | C2×C3 | semidirect |
| 30. #63802 | C2×C3 | semidirect |
| 32. #63767 | C2×C3 | semidirect |
| 217. C33 | #497 | semidirect |
| 324. C32 | C3×#497 | semidirect |
| 367. C3 | #10593291 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64228 | 2 |
| C3×#64227 | 2 |
| C3×#64222 | 2 |
| C3×#64221 | 2 |
| C3×#63802 | 2 |
| C3×#63796 | 2 |
| C3×#63767 | 2 |
| #10593291 | 3 |
| C3×#497 | 9 |