Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
424 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 120. C2×#170 | Q16 | semidirect |
| 378. C5 | #9048 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617262 | 2 |
| #10611903 | 2 |
| #10604985 | 2 |
| #10604968 | 2 |
| #10604517 | 2 |
| #10598563 | 2 |
| #10598556 | 2 |
| #9048 | 5 |