Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
740 conjugacy classes of subgroups; only the 258 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 258 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 |
|---|---|---|
| 7. C3×#5065 | C3 | direct (N × H) |
| 33. #5065 | C32 | direct (N × H) |
| 125. C33 | #499 | semidirect |
| 172. C32 | #5065 | direct (N × H) |
| 173. C32 | C3×#499 | semidirect |
| 193. C3 | C3×#5065 | direct (N × H) |
| 194. C3 | C32×#499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#125 | 2 |
| C32×#870 | 2 |
| C32×#808 | 2 |
| C32×#807 | 2 |
| C32×C4×C3⋊C8 | 2 |
| C32×#499 | 3 |
| C3×#5065 | 3 |