Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
370 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 103 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. #11720538 | C2 | semidirect |
| 4. C9×Dic3⋊C8 | C2 | semidirect |
| 6. #11720275 | C2 | semidirect |
| 7. Dic3⋊(C9⋊C8) | C2 | semidirect |
| 102. Dic3⋊C8 | D9 | semidirect |
| 203. C3×C9 | #432 | semidirect |
| 290. C9 | #4719 | semidirect |
| 329. C3 | #10588519 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Dic3×D9 | 2 |
| #11720538 | 2 |
| C3×(C2×D9)⋊C8 | 2 |
| C9×Dic3⋊C8 | 2 |
| (C2×D9)⋊(C3⋊C8) | 2 |
| #11720275 | 2 |
| Dic3⋊(C9⋊C8) | 2 |
| #10590661 | 3 |
| #10588519 | 3 |