Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1016 conjugacy classes of subgroups; only the 188 normal subgroups are shown.
This group has 1016 conjugacy classes of subgroups — too many to draw. Only its 188 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. #11723910 | C2 | semidirect |
| 3. C2×#88800 | C2 | semidirect |
| 5. C32×#803 | C2 | semidirect |
| 27. C3×#803 | D3 | semidirect |
| 78. #803 | C3⋊D3 | semidirect |
| 152. C33 | #497 | semidirect |
| 214. C32 | #4715 | semidirect |
| 215. C32 | #5060 | semidirect |
| 242. C3 | #10590372 | semidirect |
| 243. C3 | #10592414 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723910 | 2 |
| C3×#64084 | 2 |
| C2×#88800 | 2 |
| C2×#88796 | 2 |
| C32×#803 | 2 |
| #10592414 | 3 |
| #10590372 | 3 |