Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
166 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 42 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. C5×Q8×A4 | C2 | semidirect |
| 3. C5×C8×A4 | C2 | semidirect |
| 4. C22×C5×SD16 | C3 | semidirect |
| 9. A4×SD16 | C5 | direct (N × H) |
| 10. C22×C5×Q8 | C2×C3 | semidirect |
| 16. C22×C5×C8 | C2×C3 | semidirect |
| 22. Q8×A4 | C2×C5 | semidirect |
| 24. C8×A4 | C2×C5 | semidirect |
| 38. C5×SD16 | A4 | direct (N × H) |
| 41. C22×SD16 | C3×C5 | semidirect |
| 43. C5×A4 | SD16 | direct (N × H) |
| 58. C5×Q8 | C2×A4 | semidirect |
| 68. C5×C8 | C2×A4 | semidirect |
| 69. C22×Q8 | C2×C3×C5 | semidirect |
| 75. C22×C8 | C2×C3×C5 | semidirect |
| 91. C22×C5 | C3×SD16 | semidirect |
| 109. SD16 | C5×A4 | direct (N × H) |
| 114. A4 | C5×SD16 | direct (N × H) |
| 130. Q8 | C2×C5×A4 | semidirect |
| 140. C8 | C2×C5×A4 | semidirect |
| 143. C5 | A4×SD16 | direct (N × H) |
| 152. C22 | C3×C5×SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×Q8×A4 | 2 |
| C5×D4×A4 | 2 |
| C5×C8×A4 | 2 |
| C22×C5×SD16 | 3 |
| C3×C5×SD16 | 4 |
| A4×SD16 | 5 |