Finite Group DatabasebetaFinite Group DatabasebetaOrder 27008.
276 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 10. C2×Dic844 | C4 | semidirect |
| 76. C211 | #1979 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic844 | 2 |
| #27213156 | 2 |
| C2×#20269895 | 2 |
| #27213101 | 2 |
| C2×#108×C211 | 2 |
| #1979 | 211 |