Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
226 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 1. #10604448 | C2 | semidirect |
| 4. Q8⋊#674 | C2 | semidirect |
| 6. #10598522 | C2 | semidirect |
| 7. #10598512 | C2 | semidirect |
| 75. #674 | SD16 | semidirect |
| 194. C5 | #12049 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604448 | 2 |
| D4×#674 | 2 |
| SD16×#168 | 2 |
| Q8⋊#674 | 2 |
| D4⋊#674 | 2 |
| #10598522 | 2 |
| #10598512 | 2 |
| #12049 | 5 |