Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
244 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 110 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×C3×#676 | C2 | semidirect |
| 3. C3×C4×C5×C8 | C2 | semidirect |
| 4. C3×#3952 | C2 | semidirect |
| 5. C3×C4⋊#168 | C2 | semidirect |
| 6. #64977 | C3 | direct (N × H) |
| 17. C2×#676 | C2×C3 | semidirect |
| 19. C4×C5×C8 | C2×C3 | semidirect |
| 20. #3952 | C2×C3 | semidirect |
| 21. C4⋊#168 | C2×C3 | semidirect |
| 31. C3×C5×C8 | D4 | semidirect |
| 37. C3×C4×C8 | D5 | semidirect |
| 53. C3×C4×C5 | M16 | semidirect |
| 75. C5×C8 | C3×D4 | semidirect |
| 81. C4×C8 | C3×D5 | semidirect |
| 96. C3×C8 | D20 | semidirect |
| 102. C4×C5 | C3×M16 | semidirect |
| 115. C3×C5 | #436 | semidirect |
| 122. C3×C4 | #676 | semidirect |
| 139. C8 | C3×D20 | semidirect |
| 144. C5 | C3×#436 | semidirect |
| 151. C4 | C3×#676 | semidirect |
| 154. C3 | #64977 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#676 | 2 |
| C3×C4×D20 | 2 |
| C3×C4×C5×C8 | 2 |
| C3×#3952 | 2 |
| C3×C4⋊#168 | 2 |
| #64977 | 3 |
| C3×#436 | 5 |