Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1568 conjugacy classes of subgroups; only the 351 normal subgroups are shown.
This group has 1568 conjugacy classes of subgroups — too many to draw. Only its 351 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 |
|---|---|---|
| 3. C2×#88853 | C2 | semidirect |
| 4. #11723928 | C2 | semidirect |
| 6. #11722184 | C2 | semidirect |
| 7. #11722180 | C2 | semidirect |
| 127. C33 | #464 | semidirect |
| 171. C32 | #4767 | semidirect |
| 202. C3 | #10592466 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723977 | 2 |
| C2×#88861 | 2 |
| C2×#88853 | 2 |
| #11723928 | 2 |
| C33×#102 | 2 |
| #11722184 | 2 |
| #11722180 | 2 |
| #10592466 | 3 |