Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1400 conjugacy classes of subgroups; only the 349 normal subgroups are shown.
This group has 1400 conjugacy classes of subgroups — too many to draw. Only its 349 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. C2×#88863 | C2 | semidirect |
| 5. #11722206 | C2 | semidirect |
| 6. #11722194 | C2 | semidirect |
| 7. #11722192 | C2 | semidirect |
| 126. C33 | #473 | semidirect |
| 168. C32 | #5204 | semidirect |
| 195. C3 | #10592903 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#137 | 2 |
| #11723992 | 2 |
| #11723989 | 2 |
| C2×#88863 | 2 |
| #11722206 | 2 |
| #11722194 | 2 |
| #11722192 | 2 |
| #10592903 | 3 |