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×#88642 | C2 | semidirect |
| 2. C2×C3×#3664 | C2 | semidirect |
| 3. #11721037 | C2 | semidirect |
| 4. C2×#88417 | C2 | semidirect |
| 5. #11720543 | C2 | semidirect |
| 6. C9×(C2×D3)⋊C8 | C2 | semidirect |
| 7. #11720276 | C2 | semidirect |
| 35. C2×#3664 | D3 | semidirect |
| 46. C4⋊(C3⋊D9) | D4 | semidirect |
| 54. C3×Dic18 | D4 | semidirect |
| 123. (C2×D3)⋊C8 | D9 | semidirect |
| 167. Dic18 | #67 | semidirect |
| 255. C3×C9 | #449 | semidirect |
| 372. C9 | #5172 | semidirect |
| 425. C3 | #10588416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88642 | 2 |
| C2×C3×#3664 | 2 |
| #11721037 | 2 |
| C2×#88417 | 2 |
| #11720543 | 2 |
| C9×(C2×D3)⋊C8 | 2 |
| #11720276 | 2 |
| #10590823 | 3 |
| #10588416 | 3 |