Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
536 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 89 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×#88635 | C2 | semidirect |
| 2. C2×C9×#204 | C2 | semidirect |
| 3. #11721036 | C2 | semidirect |
| 4. C2×#88422 | C2 | semidirect |
| 5. #11720543 | C2 | semidirect |
| 6. C3×(C2×D9)⋊C8 | C2 | semidirect |
| 7. #11720298 | C2 | semidirect |
| 39. (C2×D9)⋊C8 | D3 | semidirect |
| 46. C4⋊(C3⋊D9) | D4 | semidirect |
| 54. C9×Dic6 | D4 | semidirect |
| 117. C2×#204 | D9 | semidirect |
| 255. C3×C9 | #449 | semidirect |
| 296. Dic6 | #611 | semidirect |
| 372. C9 | #4734 | semidirect |
| 425. C3 | #10588852 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88635 | 2 |
| C2×C9×#204 | 2 |
| #11721036 | 2 |
| C2×#88422 | 2 |
| #11720543 | 2 |
| C3×(C2×D9)⋊C8 | 2 |
| #11720298 | 2 |
| #10590823 | 3 |
| #10588852 | 3 |