Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
188 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 68 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 |
|---|---|---|
| 3. #64895 | C3 | direct (N × H) |
| 7. C3×C4×AGL(1,𝔽5) | C4 | semidirect |
| 8. C2×C3×C5×C8 | C4 | semidirect |
| 9. C2×C3×#168 | C4 | semidirect |
| 27. C4×AGL(1,𝔽5) | C3×C4 | semidirect |
| 28. C2×C5×C8 | C3×C4 | semidirect |
| 29. C2×#168 | C3×C4 | semidirect |
| 42. C2×C3×C8 | AGL(1,𝔽5) | semidirect |
| 77. C2×C8 | C3×AGL(1,𝔽5) | semidirect |
| 81. C3×C5 | H(3,ℤ/4) | semidirect |
| 103. C5 | C3×H(3,ℤ/4) | semidirect |
| 111. C3 | #64895 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4130 | 2 |
| C2×C3×#676 | 2 |
| #64895 | 3 |
| C3×H(3,ℤ/4) | 5 |