Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
248 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
| 2. C2×C3×C8×D5 | C2 | semidirect |
| 4. C3×C5×C4⋊C8 | C2 | semidirect |
| 5. C3×#3952 | C2 | semidirect |
| 6. C3×#3952 | C2 | semidirect |
| 7. C3×#3935 | C2 | semidirect |
| 8. #65125 | C3 | direct (N × H) |
| 23. C2×#676 | C2×C3 | semidirect |
| 24. C2×C8×D5 | C2×C3 | semidirect |
| 26. C5×C4⋊C8 | C2×C3 | semidirect |
| 27. #3952 | C2×C3 | semidirect |
| 28. #3952 | C2×C3 | semidirect |
| 29. #3935 | C2×C3 | semidirect |
| 45. C3×#168 | D4 | semidirect |
| 49. C3×C4⋊C8 | D5 | semidirect |
| 73. C2×C3×D5 | M16 | semidirect |
| 108. #168 | C3×D4 | semidirect |
| 112. C4⋊C8 | C3×D5 | semidirect |
| 143. C2×D5 | C3×M16 | semidirect |
| 163. C3×C5 | #435 | semidirect |
| 203. C5 | C3×#435 | semidirect |
| 217. C3 | #65125 | 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 |
| C2×C3×C8×D5 | 2 |
| C3×C4×D20 | 2 |
| C3×C5×C4⋊C8 | 2 |
| C3×#3952 | 2 |
| C3×#3935 | 2 |
| #65125 | 3 |
| C3×#435 | 5 |