Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
844 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 844 conjugacy classes of subgroups — too many to draw. Only its 166 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. C2×C33×D8 | C2 | semidirect |
| 2. C3×#64113 | C2 | semidirect |
| 3. C3×#63654 | C2 | semidirect |
| 4. C3×#63653 | C2 | semidirect |
| 5. C3×#63639 | C2 | semidirect |
| 6. #10592846 | C3 | direct (N × H) |
| 13. C3×#3746 | C22 | semidirect |
| 14. C3×#3745 | C22 | semidirect |
| 16. C3×C3⋊(C3⋊C16) | C22 | semidirect |
| 18. C2×C32×D8 | D3 | semidirect |
| 19. C2×C32×D8 | C2×C3 | semidirect |
| 20. #64113 | C2×C3 | semidirect |
| 22. #63654 | C2×C3 | semidirect |
| 23. #63653 | C2×C3 | semidirect |
| 24. #63639 | C2×C3 | semidirect |
| 54. #3746 | C22×C3 | semidirect |
| 55. #3745 | C22×C3 | semidirect |
| 60. C3⋊(C3⋊C16) | C22×C3 | semidirect |
| 71. C2×C3×D8 | C3×D3 | semidirect |
| 72. C2×C3×D8 | C3⋊D3 | semidirect |
| 153. C2×D8 | C3×C3⋊D3 | semidirect |
| 157. C33 | #509 | semidirect |
| 224. C32 | #5147 | semidirect |
| 225. C32 | C3×#509 | semidirect |
| 255. C3 | C3×#5147 | semidirect |
| 256. C3 | #10592846 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×D8 | 2 |
| C3×#64113 | 2 |
| C3×#63654 | 2 |
| C3×#63653 | 2 |
| C3×#63639 | 2 |
| #10592846 | 3 |
| C3×#5147 | 3 |