Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
596 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 136 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. C2×D4×D15 | C2 | semidirect |
| 2. C2×#6768 | C2 | semidirect |
| 3. C2×C5×#213 | C2 | semidirect |
| 4. C2×C3×#687 | C2 | semidirect |
| 5. #91500 | C2 | direct (N × H) |
| 6. C2×#6658 | C2 | semidirect |
| 7. C2×#6654 | C2 | semidirect |
| 8. C2×#6651 | C2 | semidirect |
| 14. D4×D15 | C22 | semidirect |
| 17. C2×C5×D12 | C22 | semidirect |
| 18. C2×C3×Dic10 | C22 | semidirect |
| 22. #6768 | C22 | semidirect |
| 23. C5×#213 | C22 | semidirect |
| 24. C2×C5×C3⋊C8 | C22 | semidirect |
| 25. C3×#687 | C22 | semidirect |
| 26. C2×C3×#168 | C22 | semidirect |
| 27. #6658 | C22 | semidirect |
| 28. #6654 | C22 | semidirect |
| 29. #6651 | C22 | semidirect |
| 34. C2×#687 | D3 | semidirect |
| 55. C5×D12 | C23 | semidirect |
| 58. C3×Dic10 | C23 | semidirect |
| 61. C3×#168 | C23 | semidirect |
| 62. C5×C3⋊C8 | C23 | semidirect |
| 67. C2×#213 | D5 | semidirect |
| 83. C2×Dic10 | C2×D3 | semidirect |
| 86. #687 | C2×D3 | semidirect |
| 88. C2×#168 | C2×D3 | semidirect |
| 116. C2×D12 | C2×D5 | semidirect |
| 122. #213 | C2×D5 | semidirect |
| 123. C2×C3⋊C8 | C2×D5 | semidirect |
| 147. Dic10 | C22×D3 | semidirect |
| 149. #168 | C22×D3 | semidirect |
| 159. C2×C3×C5 | AGL(1,ℤ/8) | semidirect |
| 182. D12 | C22×D5 | semidirect |
| 187. C3⋊C8 | C22×D5 | semidirect |
| 222. C3×C5 | C2×AGL(1,ℤ/8) | semidirect |
| 239. C2×C5 | #914 | semidirect |
| 268. C2×C3 | #4057 | semidirect |
| 273. C5 | C2×#914 | semidirect |
| 288. C3 | C2×#4057 | semidirect |
| 293. C2 | #91500 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×D15 | 2 |
| C2×#6768 | 2 |
| C2×C5×#213 | 2 |
| C2×C3×#687 | 2 |
| #91500 | 2 |
| C2×#6658 | 2 |
| C2×#6654 | 2 |
| C2×#6651 | 2 |
| C2×#4057 | 3 |
| C2×#914 | 5 |