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. #11723443 | C2 | semidirect |
| 5. C2×#88799 | C2 | semidirect |
| 6. C2×#88798 | C2 | semidirect |
| 7. #11722019 | C2 | semidirect |
| 215. C33 | #497 | semidirect |
| 303. C32 | #5060 | semidirect |
| 304. C32 | #5167 | semidirect |
| 340. C3 | #10591491 | semidirect |
| 341. C3 | #10592759 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88861 | 2 |
| C2×C3×#3754 | 2 |
| C32×#936 | 2 |
| #11723443 | 2 |
| C2×#88799 | 2 |
| C2×#88798 | 2 |
| #11722019 | 2 |
| #10592759 | 3 |
| #10591491 | 3 |