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 |
|---|---|---|
| 4. #11723455 | C2 | semidirect |
| 5. C2×#88800 | C2 | semidirect |
| 6. C2×#88798 | C2 | semidirect |
| 7. #11722020 | C2 | semidirect |
| 215. C33 | #497 | semidirect |
| 303. C32 | #5060 | semidirect |
| 304. C32 | #5167 | semidirect |
| 340. C3 | #10591491 | semidirect |
| 341. C3 | #10592866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88861 | 2 |
| C3×#64145 | 2 |
| C2×C32×#214 | 2 |
| #11723455 | 2 |
| C2×#88800 | 2 |
| C2×#88798 | 2 |
| #11722020 | 2 |
| #10592866 | 3 |
| #10591491 | 3 |