Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
390 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 85 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. C2×#88547 | C2 | semidirect |
| 5. C3×#63395 | C2 | semidirect |
| 6. #11720269 | C2 | semidirect |
| 7. #11720265 | C2 | semidirect |
| 35. #63395 | D3 | semidirect |
| 218. C3×C9 | #470 | semidirect |
| 310. C9 | #4816 | semidirect |
| 349. C3 | #10588728 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88547 | 2 |
| C9×#946 | 2 |
| #11720961 | 2 |
| C2×#88420 | 2 |
| C3×#63395 | 2 |
| #11720269 | 2 |
| #11720265 | 2 |
| #10591598 | 3 |
| #10588728 | 3 |