Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1260 conjugacy classes of subgroups; only the 349 normal subgroups are shown.
This group has 1260 conjugacy classes of subgroups — too many to draw. Only its 349 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 |
|---|---|---|
| 112. C33 | #491 | semidirect |
| 149. C32 | #4797 | semidirect |
| 175. C3 | #10592496 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723985 | 2 |
| #11723931 | 2 |
| C33×#103 | 2 |
| #11722205 | 2 |
| #11722186 | 2 |
| #11722185 | 2 |
| #11722180 | 2 |
| #10592496 | 3 |