Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
380 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 95 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. #11721865 | C2 | semidirect |
| 3. #11720859 | C2 | semidirect |
| 4. C9×#837 | C2 | semidirect |
| 5. #11720285 | C2 | semidirect |
| 6. #11720260 | C2 | semidirect |
| 7. Dic3×C9⋊C8 | C2 | semidirect |
| 16. C3×#3675 | C4 | semidirect |
| 17. C3×#3674 | C4 | semidirect |
| 18. C3×#3673 | C4 | semidirect |
| 19. C3×#3672 | C4 | semidirect |
| 78. #3675 | Dic3 | semidirect |
| 79. #3674 | Dic3 | semidirect |
| 80. #3673 | Dic3 | semidirect |
| 81. #3672 | Dic3 | semidirect |
| 110. #837 | D9 | semidirect |
| 224. C3×C9 | #443 | semidirect |
| 314. C9 | #5196 | semidirect |
| 351. C3 | #10588504 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721865 | 2 |
| C3×#63513 | 2 |
| #11720859 | 2 |
| C9×#837 | 2 |
| #11720285 | 2 |
| #11720260 | 2 |
| Dic3×C9⋊C8 | 2 |
| #10591675 | 3 |
| #10588504 | 3 |