Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
516 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 214 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×#4150 | C2 | semidirect |
| 2. C3×#4149 | C2 | semidirect |
| 3. C3×C5×#131 | C2 | semidirect |
| 4. C3×#4055 | C2 | semidirect |
| 5. C3×#4054 | C2 | semidirect |
| 6. C3×#4050 | C2 | semidirect |
| 7. C2×C3×#677 | C2 | semidirect |
| 8. #66085 | C3 | direct (N × H) |
| 15. C3×#709 | C22 | semidirect |
| 17. C2×C3×Dic10 | C22 | semidirect |
| 18. C3×C5×M16 | C22 | semidirect |
| 19. C2×C3×C5×C8 | C22 | semidirect |
| 20. C3×Dic20 | C22 | semidirect |
| 21. C3×D40 | C22 | semidirect |
| 22. C3×#677 | C22 | semidirect |
| 23. C3×#677 | C22 | semidirect |
| 24. C3×#677 | C22 | semidirect |
| 26. #4150 | C2×C3 | semidirect |
| 27. #4149 | C2×C3 | semidirect |
| 28. C5×#131 | C2×C3 | semidirect |
| 29. #4055 | C2×C3 | semidirect |
| 30. #4054 | C2×C3 | semidirect |
| 31. #4050 | C2×C3 | semidirect |
| 32. C2×#677 | C2×C3 | semidirect |
| 56. C3×#131 | D5 | semidirect |
| 63. #709 | C22×C3 | semidirect |
| 65. C2×Dic10 | C22×C3 | semidirect |
| 66. C5×M16 | C22×C3 | semidirect |
| 67. C2×C5×C8 | C22×C3 | semidirect |
| 68. Dic20 | C22×C3 | semidirect |
| 69. D40 | C22×C3 | semidirect |
| 70. #677 | C22×C3 | semidirect |
| 71. #677 | C22×C3 | semidirect |
| 72. #677 | C22×C3 | semidirect |
| 96. C3×M16 | C2×D5 | semidirect |
| 97. C2×C3×C8 | C2×D5 | semidirect |
| 121. #131 | C3×D5 | semidirect |
| 165. M16 | C2×C3×D5 | semidirect |
| 166. C2×C8 | C2×C3×D5 | semidirect |
| 167. C3×C5 | #577 | semidirect |
| 201. C5 | C3×#577 | semidirect |
| 210. C3 | #66085 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4150 | 2 |
| C3×#4149 | 2 |
| C3×C5×#131 | 2 |
| C3×#4055 | 2 |
| C3×#4054 | 2 |
| C3×#4050 | 2 |
| C2×C3×#677 | 2 |
| #66085 | 3 |
| C3×#577 | 5 |