Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
516 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 144 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. C2×D5×Dic6 | C2 | semidirect |
| 3. C2×#6718 | C2 | semidirect |
| 4. C2×C5×#216 | C2 | semidirect |
| 5. #91508 | C2 | direct (N × H) |
| 6. C2×#6657 | C2 | semidirect |
| 7. C2×#6655 | C2 | semidirect |
| 8. C2×#6649 | C2 | semidirect |
| 22. D5×Dic6 | C22 | semidirect |
| 23. #6718 | C22 | semidirect |
| 25. C5×#216 | C22 | semidirect |
| 27. #6657 | C22 | semidirect |
| 28. #6655 | C22 | semidirect |
| 29. #6649 | C22 | semidirect |
| 66. C2×#216 | D5 | semidirect |
| 116. #216 | C2×D5 | semidirect |
| 153. C2×C3×C5 | #137 | semidirect |
| 211. C3×C5 | C2×#137 | semidirect |
| 223. C2×C5 | #951 | semidirect |
| 252. C2×C3 | #4064 | semidirect |
| 254. C5 | C2×#951 | semidirect |
| 266. C3 | C2×#4064 | semidirect |
| 269. C2 | #91508 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#713 | 2 |
| C2×D5×Dic6 | 2 |
| C2×#6718 | 2 |
| C2×C5×#216 | 2 |
| #91508 | 2 |
| C2×#6657 | 2 |
| C2×#6655 | 2 |
| C2×#6649 | 2 |
| C2×#4064 | 3 |
| C2×#951 | 5 |