Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
390 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 4. #11720526 | C2 | semidirect |
| 5. C3×#63367 | C2 | semidirect |
| 6. #11720263 | C2 | semidirect |
| 7. #11720262 | C2 | semidirect |
| 21. #88420 | C4 | semidirect |
| 34. #63367 | D3 | semidirect |
| 47. C3⋊(C9⋊C8) | C2×C4 | semidirect |
| 48. C3×C9⋊C8 | C2×C4 | semidirect |
| 131. C9⋊C8 | C4×D3 | semidirect |
| 198. C3×C9 | #428 | semidirect |
| 279. C9 | #4861 | semidirect |
| 315. C3 | #10588679 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#892 | 2 |
| D3×C4⋊Dic9 | 2 |
| C2×#88420 | 2 |
| #11720526 | 2 |
| C3×#63367 | 2 |
| #11720263 | 2 |
| #11720262 | 2 |
| #10590437 | 3 |
| #10588679 | 3 |