Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
220 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 9. #20269913 | C4 | semidirect |
| 15. #108×C211 | C4 | semidirect |
| 58. C211 | #1778 | semidirect |
| 71. #108 | Dic211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269913 | 2 |
| M16×Dic211 | 2 |
| C2×#20269887 | 2 |
| #27212910 | 2 |
| C2×#108×C211 | 2 |
| #1778 | 211 |