Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1198 conjugacy classes of subgroups; only the 236 normal subgroups are shown.
This group has 1198 conjugacy classes of subgroups — too many to draw. Only its 236 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 |
|---|---|---|
| 2. C2×C22⋊#674 | C2 | semidirect |
| 7. C22×#674 | C22 | semidirect |
| 27. C24×C5 | C16 | semidirect |
| 88. C22×C5 | C22⋊C16 | semidirect |
| 97. C24 | #674 | semidirect |
| 138. C5 | #12679 | semidirect |
| 144. C22 | C22⋊#674 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×#168 | 2 |
| C2×C22⋊#674 | 2 |
| #12679 | 5 |