Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
360 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 54 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×#63809 | C2 | semidirect |
| 2. C3×#63797 | C2 | semidirect |
| 3. C3×#63765 | C2 | semidirect |
| 4. C3×#63735 | C2 | semidirect |
| 5. C3×#63734 | C2 | semidirect |
| 6. #10593277 | C3 | direct (N × H) |
| 12. C3×#3718 | C22 | semidirect |
| 14. C3×#3713 | C22 | semidirect |
| 15. C3×#3708 | C22 | semidirect |
| 18. #63809 | C2×C3 | semidirect |
| 19. #63797 | C2×C3 | semidirect |
| 20. #63765 | C2×C3 | semidirect |
| 21. #63735 | C2×C3 | semidirect |
| 22. #63734 | C2×C3 | semidirect |
| 53. #3718 | C22×C3 | semidirect |
| 55. #3713 | C22×C3 | semidirect |
| 56. #3708 | C22×C3 | semidirect |
| 162. C33 | #509 | semidirect |
| 250. C32 | C3×#509 | semidirect |
| 288. C3 | #10593277 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63809 | 2 |
| C3×#63797 | 2 |
| C3×#63765 | 2 |
| C3×#63735 | 2 |
| C3×#63734 | 2 |
| #10593277 | 3 |
| C3×#509 | 9 |