Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
720 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 720 conjugacy classes of subgroups — too many to draw. Only its 152 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 |
|---|---|---|
| 1. C2×C3×#3746 | C2 | semidirect |
| 4. #11722189 | C2 | semidirect |
| 5. #11722029 | C2 | semidirect |
| 21. C2×#3746 | D3 | semidirect |
| 161. C33 | #473 | semidirect |
| 225. C32 | #5143 | semidirect |
| 226. C32 | #5192 | semidirect |
| 254. C3 | #10590930 | semidirect |
| 255. C3 | #10592842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#3746 | 2 |
| C32×#901 | 2 |
| #11723373 | 2 |
| #11722189 | 2 |
| #11722029 | 2 |
| #10592842 | 3 |
| #10590930 | 3 |