Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
186 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 186 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×D4×A4 | C2 | semidirect |
| 2. C5×C8×A4 | C2 | semidirect |
| 3. C22×C5×D8 | C3 | semidirect |
| 7. A4×D8 | C5 | direct (N × H) |
| 8. C22×C5×D4 | C2×C3 | semidirect |
| 12. C22×C5×C8 | C2×C3 | semidirect |
| 17. D4×A4 | C2×C5 | semidirect |
| 18. C8×A4 | C2×C5 | semidirect |
| 27. C5×D8 | A4 | direct (N × H) |
| 30. C22×D8 | C3×C5 | semidirect |
| 32. C5×A4 | D8 | direct (N × H) |
| 45. C5×D4 | C2×A4 | semidirect |
| 49. C5×C8 | C2×A4 | semidirect |
| 50. C22×D4 | C2×C3×C5 | semidirect |
| 54. C22×C8 | C2×C3×C5 | semidirect |
| 69. C22×C5 | C3×D8 | semidirect |
| 80. D8 | C5×A4 | direct (N × H) |
| 85. A4 | C5×D8 | direct (N × H) |
| 100. D4 | C2×C5×A4 | semidirect |
| 104. C8 | C2×C5×A4 | semidirect |
| 107. C5 | A4×D8 | direct (N × H) |
| 116. C22 | C3×C5×D8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D4×A4 | 2 |
| C5×C8×A4 | 2 |
| C22×C5×D8 | 3 |
| C3×C5×D8 | 4 |
| A4×D8 | 5 |