Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
440 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 85 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×C3×#3663 | C2 | semidirect |
| 2. #11721036 | C2 | semidirect |
| 3. #11721004 | C2 | semidirect |
| 4. C2×#88422 | C2 | semidirect |
| 5. #11720543 | C2 | semidirect |
| 6. C9×#821 | C2 | semidirect |
| 7. #11720264 | C2 | semidirect |
| 32. C2×#3663 | D3 | semidirect |
| 54. C3×C9⋊C8 | D4 | semidirect |
| 113. #821 | D9 | semidirect |
| 155. C9⋊C8 | #67 | semidirect |
| 236. C3×C9 | #469 | semidirect |
| 345. C9 | #5135 | semidirect |
| 395. C3 | #10588462 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#3663 | 2 |
| #11721036 | 2 |
| #11721004 | 2 |
| C2×#88422 | 2 |
| #11720543 | 2 |
| C9×#821 | 2 |
| #11720264 | 2 |
| #10590827 | 3 |
| #10588462 | 3 |