Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
228 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 7. C4⋊ΓL(1,𝔽16) | C4 | semidirect |
| 8. C2×C3×C5×C8 | C4 | semidirect |
| 9. C2×C3×#168 | C4 | semidirect |
| 30. C2×C5×C8 | Dic3 | semidirect |
| 31. C2×#168 | Dic3 | semidirect |
| 47. C2×C3×C8 | AGL(1,𝔽5) | semidirect |
| 90. C2×C8 | ΓL(1,𝔽16) | semidirect |
| 93. C3×C5 | #340 | semidirect |
| 123. C5 | #4551 | semidirect |
| 133. C3 | #64893 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊ΓL(1,𝔽16) | 2 |
| C2×C3×C8×D5 | 2 |
| #64893 | 3 |
| #4551 | 5 |