Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
185 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 185 conjugacy classes of subgroups — too many to draw. Only its 45 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. #11720660 | C2 | semidirect |
| 2. #131⋊C27 | C2 | semidirect |
| 45. #576 | C27 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11720660 | 2 |
| #131⋊C27 | 2 |
| C9×#576 | 3 |
| Q16×C27 | 4 |