Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
532 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 532 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 |
|---|---|---|
| 1. C2×#6769 | C2 | semidirect |
| 2. C2×#6765 | C2 | semidirect |
| 3. C2×#6706 | C2 | semidirect |
| 4. C2×C5×D3×C8 | C2 | semidirect |
| 5. C2×C3×#677 | C2 | semidirect |
| 6. C2×#6662 | C2 | semidirect |
| 7. C2×#6653 | C2 | semidirect |
| 8. #91272 | C2 | direct (N × H) |
| 20. #6769 | C22 | semidirect |
| 22. #6765 | C22 | semidirect |
| 24. #6706 | C22 | semidirect |
| 26. C5×D3×C8 | C22 | semidirect |
| 27. C3×#677 | C22 | semidirect |
| 28. #6662 | C22 | semidirect |
| 29. #6653 | C22 | semidirect |
| 38. C2×#677 | D3 | semidirect |
| 69. C2×D3×C8 | D5 | semidirect |
| 89. #677 | C2×D3 | semidirect |
| 122. D3×C8 | C2×D5 | semidirect |
| 154. C2×C3×C5 | #135 | semidirect |
| 214. C3×C5 | C2×#135 | semidirect |
| 228. C2×C5 | #916 | semidirect |
| 256. C2×C3 | #4050 | semidirect |
| 260. C5 | C2×#916 | semidirect |
| 273. C3 | C2×#4050 | semidirect |
| 277. C2 | #91272 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6769 | 2 |
| C2×#6765 | 2 |
| C2×#6706 | 2 |
| C2×C5×D3×C8 | 2 |
| C2×C3×#677 | 2 |
| C2×#6662 | 2 |
| C2×#6653 | 2 |
| #91272 | 2 |
| C2×#4050 | 3 |
| C2×#916 | 5 |