Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
368 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 83 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. C9×#892 | C2 | semidirect |
| 3. #11720528 | C2 | semidirect |
| 4. C3×#63367 | C2 | semidirect |
| 5. (C2×D3)⋊(C9⋊C8) | C2 | semidirect |
| 6. #11720267 | C2 | semidirect |
| 7. #11720263 | C2 | semidirect |
| 34. #63367 | D3 | semidirect |
| 93. #892 | D9 | semidirect |
| 210. C3×C9 | #482 | semidirect |
| 305. C9 | #4866 | semidirect |
| 348. C3 | #10588684 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#892 | 2 |
| #11721038 | 2 |
| #11720528 | 2 |
| C3×#63367 | 2 |
| (C2×D3)⋊(C9⋊C8) | 2 |
| #11720267 | 2 |
| #11720263 | 2 |
| #10590425 | 3 |
| #10588684 | 3 |