Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
186 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 12. #20269910 | C4 | semidirect |
| 13. #20269910 | C4 | semidirect |
| 14. #20269908 | C4 | semidirect |
| 15. #20269908 | C4 | semidirect |
| 88. C211 | #1922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27213182 | 2 |
| #27213101 | 2 |
| #27212910 | 2 |
| #27212907 | 2 |
| #27212905 | 2 |
| #27212900 | 2 |
| #424×C211 | 2 |
| #1922 | 211 |