Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1016 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 1016 conjugacy classes of subgroups — too many to draw. Only its 158 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. #11723985 | C2 | semidirect |
| 2. C2×C3×#3756 | C2 | semidirect |
| 5. C2×#88800 | C2 | semidirect |
| 7. #11722021 | C2 | semidirect |
| 27. C2×#3756 | D3 | semidirect |
| 215. C33 | #497 | semidirect |
| 302. C32 | #5167 | semidirect |
| 303. C32 | #5190 | semidirect |
| 338. C3 | #10591611 | semidirect |
| 339. C3 | #10592866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723985 | 2 |
| C2×C3×#3756 | 2 |
| C2×C32×#215 | 2 |
| #11723434 | 2 |
| C2×#88800 | 2 |
| C2×#88794 | 2 |
| #11722021 | 2 |
| #10592866 | 3 |
| #10591611 | 3 |