Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
524 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 524 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 |
|---|---|---|
| 2. C2×#88524 | C2 | semidirect |
| 3. #11720961 | C2 | semidirect |
| 4. C2×#88418 | C2 | semidirect |
| 5. C9×(C2×D3)⋊C8 | C2 | semidirect |
| 6. C3×#63376 | C2 | semidirect |
| 7. #11720284 | C2 | semidirect |
| 39. #63376 | D3 | semidirect |
| 120. (C2×D3)⋊C8 | D9 | semidirect |
| 249. C3×C9 | #452 | semidirect |
| 360. C9 | #4808 | semidirect |
| 408. C3 | #10588415 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88642 | 2 |
| C2×#88524 | 2 |
| #11720961 | 2 |
| C2×#88418 | 2 |
| C9×(C2×D3)⋊C8 | 2 |
| C3×#63376 | 2 |
| #11720284 | 2 |
| #10590970 | 3 |
| #10588415 | 3 |