Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
176 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 54 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. #65774 | C2 | semidirect |
| 2. #65705 | C2 | semidirect |
| 4. D4⋊#170 | C2 | semidirect |
| 5. #64883 | C2 | semidirect |
| 6. #64879 | C2 | semidirect |
| 7. #64871 | C2 | semidirect |
| 71. #168 | M16 | semidirect |
| 147. C5 | #1594 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65774 | 2 |
| #65705 | 2 |
| #65045 | 2 |
| D4⋊#170 | 2 |
| #64883 | 2 |
| #64879 | 2 |
| #64871 | 2 |
| #1594 | 5 |