Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2128 conjugacy classes of subgroups; only the 515 normal subgroups are shown.
This group has 2128 conjugacy classes of subgroups — too many to draw. Only its 515 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 |
|---|---|---|
| 2. C2×#88863 | C2 | semidirect |
| 3. C2×#88861 | C2 | semidirect |
| 4. #11723965 | C2 | semidirect |
| 5. #11722205 | C2 | semidirect |
| 6. #11722202 | C2 | semidirect |
| 7. #11722200 | C2 | semidirect |
| 146. C33 | #452 | semidirect |
| 199. C32 | #5239 | semidirect |
| 237. C3 | #10592938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×#41 | 2 |
| C2×#88863 | 2 |
| C2×#88861 | 2 |
| #11723965 | 2 |
| #11722205 | 2 |
| #11722202 | 2 |
| #11722200 | 2 |
| #10592938 | 3 |