Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
268 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 118 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 |
|---|---|---|
| 2. C3×D4×Dic5 | C2 | semidirect |
| 3. C3×#3964 | C2 | semidirect |
| 4. C3×#3950 | C2 | semidirect |
| 5. C3×C8×Dic5 | C2 | semidirect |
| 6. D8×Dic5 | C3 | direct (N × H) |
| 9. C3×C5×D8 | C4 | semidirect |
| 17. D4×Dic5 | C2×C3 | semidirect |
| 18. #3964 | C2×C3 | semidirect |
| 19. #3950 | C2×C3 | semidirect |
| 20. C8×Dic5 | C2×C3 | semidirect |
| 23. C3×C5×D4 | C2×C4 | semidirect |
| 29. C3×C5×C8 | C2×C4 | semidirect |
| 38. C5×D8 | C3×C4 | semidirect |
| 53. C3×Dic5 | D8 | direct (N × H) |
| 56. C3×D8 | Dic5 | direct (N × H) |
| 64. C5×D4 | C2×C3×C4 | semidirect |
| 70. C5×C8 | C2×C3×C4 | semidirect |
| 83. C3×D4 | C2×Dic5 | semidirect |
| 90. C3×C8 | C2×Dic5 | semidirect |
| 99. Dic5 | C3×D8 | direct (N × H) |
| 102. D8 | C3×Dic5 | direct (N × H) |
| 108. C3×C5 | C4×D8 | semidirect |
| 124. D4 | C2×C3×Dic5 | semidirect |
| 131. C8 | C2×C3×Dic5 | semidirect |
| 136. C5 | C3×C4×D8 | semidirect |
| 146. C3 | D8×Dic5 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×D8 | 2 |
| C3×D4×Dic5 | 2 |
| C3×#3964 | 2 |
| C3×#3950 | 2 |
| C3×C8×Dic5 | 2 |
| D8×Dic5 | 3 |
| C3×C4×D8 | 5 |