Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
532 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 160 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×#6817 | C2 | semidirect |
| 2. C2×C3×#709 | C2 | semidirect |
| 3. C22×C5×C3⋊C8 | C2 | semidirect |
| 4. C2×#6662 | C2 | semidirect |
| 5. C2×#6658 | C2 | semidirect |
| 6. #91311 | C2 | direct (N × H) |
| 7. C2×#6657 | C2 | semidirect |
| 8. C2×#6653 | C2 | semidirect |
| 13. #6817 | C22 | semidirect |
| 19. C3×#709 | C22 | semidirect |
| 25. C2×C5×C3⋊C8 | C22 | semidirect |
| 26. #6662 | C22 | semidirect |
| 27. #6658 | C22 | semidirect |
| 28. #6657 | C22 | semidirect |
| 29. #6653 | C22 | semidirect |
| 32. C2×#709 | D3 | semidirect |
| 69. C22×C3⋊C8 | D5 | semidirect |
| 76. #709 | C2×D3 | semidirect |
| 122. C2×C3⋊C8 | C2×D5 | semidirect |
| 155. C2×C3×C5 | #135 | semidirect |
| 214. C3×C5 | C2×#135 | semidirect |
| 228. C2×C5 | #950 | semidirect |
| 257. C2×C3 | #4050 | semidirect |
| 260. C5 | C2×#950 | semidirect |
| 273. C3 | C2×#4050 | semidirect |
| 277. C2 | #91311 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6817 | 2 |
| C2×C3×#709 | 2 |
| C22×C5×C3⋊C8 | 2 |
| C2×#6662 | 2 |
| C2×#6658 | 2 |
| #91311 | 2 |
| C2×#6657 | 2 |
| C2×#6653 | 2 |
| C2×#4050 | 3 |
| C2×#950 | 5 |