Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
162 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 65 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. #20269887 | C4 | semidirect |
| 13. C8×Dic211 | C4 | semidirect |
| 72. C211 | #1841 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| M16×Dic211 | 2 |
| #27212917 | 2 |
| #27212907 | 2 |
| #27212905 | 2 |
| C211⋊#338 | 2 |
| #27212902 | 2 |
| #344×C211 | 2 |
| #1841 | 211 |