Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
434 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 93 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. #11721813 | C2 | semidirect |
| 3. C2×C3×#3667 | C2 | semidirect |
| 4. C2×#88424 | C2 | semidirect |
| 5. #11720295 | C2 | semidirect |
| 6. #11720269 | C2 | semidirect |
| 7. #11720262 | C2 | semidirect |
| 34. C2×#3667 | D3 | semidirect |
| 53. C3×C9⋊C8 | D4 | semidirect |
| 155. C9⋊C8 | #67 | semidirect |
| 235. C3×C9 | #468 | semidirect |
| 341. C9 | #5134 | semidirect |
| 386. C3 | #10588718 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721813 | 2 |
| C9×#930 | 2 |
| C2×C3×#3667 | 2 |
| C2×#88424 | 2 |
| #11720295 | 2 |
| #11720269 | 2 |
| #11720262 | 2 |
| #10591176 | 3 |
| #10588718 | 3 |