Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
264 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 102 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. C3×C4×C5×D4 | C2 | semidirect |
| 3. C3×C4×D20 | C2 | semidirect |
| 4. C3×#3964 | C2 | semidirect |
| 5. C3×#3941 | C2 | semidirect |
| 6. C3×#3940 | C2 | semidirect |
| 7. C3×#3935 | C2 | semidirect |
| 8. #65303 | C3 | direct (N × H) |
| 16. C3×#686 | C4 | semidirect |
| 22. C4×C5×D4 | C2×C3 | semidirect |
| 24. C4×D20 | C2×C3 | semidirect |
| 25. #3964 | C2×C3 | semidirect |
| 26. #3941 | C2×C3 | semidirect |
| 27. #3940 | C2×C3 | semidirect |
| 28. #3935 | C2×C3 | semidirect |
| 32. C3×C5×D4 | C2×C4 | semidirect |
| 40. C3×D20 | C2×C4 | semidirect |
| 43. C3×#168 | C2×C4 | semidirect |
| 46. C3×C4×D4 | D5 | semidirect |
| 58. #686 | C3×C4 | semidirect |
| 92. C5×D4 | C2×C3×C4 | semidirect |
| 100. D20 | C2×C3×C4 | semidirect |
| 103. #168 | C2×C3×C4 | semidirect |
| 106. C4×D4 | C3×D5 | semidirect |
| 121. C3×D4 | C4×D5 | semidirect |
| 156. C3×C5 | #442 | semidirect |
| 180. D4 | C3×C4×D5 | semidirect |
| 195. C5 | C3×#442 | semidirect |
| 209. C3 | #65303 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C5×D4 | 2 |
| C2×C3×#686 | 2 |
| C3×C4×D20 | 2 |
| C3×#3964 | 2 |
| C3×#3941 | 2 |
| C3×#3940 | 2 |
| C3×#3935 | 2 |
| #65303 | 3 |
| C3×#442 | 5 |