Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
248 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 78 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. C2×D3×#168 | C2 | semidirect |
| 4. #91098 | C2 | semidirect |
| 5. C5×(C2×D3)⋊C8 | C2 | semidirect |
| 6. #90955 | C2 | semidirect |
| 7. #90954 | C2 | semidirect |
| 25. C2×#676 | D3 | semidirect |
| 44. C3×#168 | D4 | semidirect |
| 50. (C2×D3)⋊C8 | D5 | semidirect |
| 70. C2×C5×D3 | M16 | semidirect |
| 108. #168 | #67 | semidirect |
| 163. C3×C5 | #435 | semidirect |
| 170. C2×D3 | #676 | semidirect |
| 203. C5 | #5127 | semidirect |
| 217. C3 | #65019 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#676 | 2 |
| C4×#1201 | 2 |
| C2×D3×#168 | 2 |
| #91098 | 2 |
| C5×(C2×D3)⋊C8 | 2 |
| #90955 | 2 |
| #90954 | 2 |
| #65019 | 3 |
| #5127 | 5 |