Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
302 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 108. C33 | #364 | semidirect |
| 165. C32 | #4463 | semidirect |
| 166. C32 | #4511 | semidirect |
| 189. C3 | #10589134 | semidirect |
| 190. C3 | #10589135 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C8×C3⋊Dic3 | 2 |
| C3×#63639 | 2 |
| #10589135 | 3 |
| #10589134 | 3 |