Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
292 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 292 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 |
|---|---|---|
| 25. C2×Dic422 | C8 | semidirect |
| 35. C2×C211⋊C8 | Q8 | semidirect |
| 51. C2×C8×C211 | Q8 | semidirect |
| 108. C211 | #1984 | semidirect |
| 153. C2×C8 | Dic422 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic422 | 2 |
| C2×Dic211⋊C8 | 2 |
| C2×C8×Dic211 | 2 |
| #27212901 | 2 |
| #27212900 | 2 |
| #336×C211 | 2 |
| #1984 | 211 |