Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
378 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 83 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. C3×#63644 | C2 | semidirect |
| 3. C3×#63639 | C2 | semidirect |
| 10. C3×#3746 | C4 | semidirect |
| 11. C3×#3745 | C4 | semidirect |
| 18. #63644 | D3 | semidirect |
| 19. #63639 | D3 | semidirect |
| 49. #3746 | Dic3 | semidirect |
| 50. #3745 | Dic3 | semidirect |
| 198. C33 | #360 | semidirect |
| 302. C32 | #4488 | semidirect |
| 303. C32 | #4518 | semidirect |
| 304. C32 | #4566 | semidirect |
| 341. C3 | #10589123 | semidirect |
| 342. C3 | #10589124 | semidirect |
| 343. C3 | #10589125 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64113 | 2 |
| C3×#63644 | 2 |
| C3×#63639 | 2 |
| #10589125 | 3 |
| #10589124 | 3 |
| #10589123 | 3 |