Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
180 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 39 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 |
|---|---|---|
| 60. C33 | #368 | semidirect |
| 92. C32 | #4506 | semidirect |
| 108. C3 | #10590070 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#3708 | 2 |
| #11722081 | 2 |
| #10590070 | 3 |
| #4506 | 9 |