Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
230 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 48 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 |
|---|---|---|
| 127. C33 | #479 | semidirect |
| 183. C32 | #4829 | semidirect |
| 215. C3 | #10593560 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11724361 | 2 |
| Dic6×#157 | 2 |
| #11722808 | 2 |
| #11722806 | 2 |
| C3×#63744 | 2 |
| #11722709 | 2 |
| #10593560 | 3 |
| #4829 | 9 |