Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
180 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 2. C2×C3×#674 | C2 | semidirect |
| 3. C3×#3990 | C2 | direct (N × H) |
| 4. C2×#3990 | C3 | direct (N × H) |
| 10. C3×#674 | C22 | semidirect |
| 13. C2×#674 | C2×C3 | semidirect |
| 14. #3990 | C2×C3 | direct (N × H) |
| 31. #674 | C22×C3 | semidirect |
| 56. C2×C3×C5 | M32 | semidirect |
| 79. C3×C5 | C2×M32 | semidirect |
| 86. C2×C5 | C3×M32 | semidirect |
| 98. C2×C3 | #3990 | direct (N × H) |
| 100. C5 | C2×C3×M32 | semidirect |
| 107. C3 | C2×#3990 | direct (N × H) |
| 109. C2 | C3×#3990 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C8×D5 | 2 |
| C2×C3×#674 | 2 |
| C3×#3990 | 2 |
| C2×#3990 | 3 |
| C2×C3×M32 | 5 |