Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1260 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1260 conjugacy classes of subgroups — too many to draw. Only its 251 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×C9×#126 | C2 | semidirect |
| 2. #11721751 | C2 | semidirect |
| 3. #11721750 | C2 | semidirect |
| 4. #11721730 | C2 | semidirect |
| 5. #11721728 | C2 | semidirect |
| 6. #11721713 | C2 | semidirect |
| 7. #11721711 | C2 | semidirect |
| 14. C2×C4⋊(C3⋊D9) | C22 | semidirect |
| 15. C2×C4×C3⋊D9 | C22 | semidirect |
| 16. C3×C9×C4⋊C4 | C22 | semidirect |
| 18. C3×C42×C9 | C22 | semidirect |
| 21. #88536 | C22 | semidirect |
| 22. #88534 | C22 | semidirect |
| 30. C9×#126 | D3 | semidirect |
| 71. C9×C4⋊C4 | C2×D3 | semidirect |
| 73. C42×C9 | C2×D3 | semidirect |
| 89. C3×#126 | D9 | semidirect |
| 147. C3×C4⋊C4 | C2×D9 | semidirect |
| 151. C3×C42 | C2×D9 | semidirect |
| 185. #126 | C3⋊D9 | semidirect |
| 190. C3×C9 | #560 | semidirect |
| 234. C4⋊C4 | C2×C3⋊D9 | semidirect |
| 239. C42 | C2×C3⋊D9 | semidirect |
| 263. C9 | #5711 | semidirect |
| 298. C3 | #10589813 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×#126 | 2 |
| #11721751 | 2 |
| #11721750 | 2 |
| #11721730 | 2 |
| #11721728 | 2 |
| #11721713 | 2 |
| #11721711 | 2 |
| #10596182 | 3 |
| #10589813 | 3 |