Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
180 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 131 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. #91096 | C2 | direct (N × H) |
| 3. C2×C3⋊#672 | C2 | semidirect |
| 10. C3⋊#672 | C22 | semidirect |
| 57. C2×C3×C5 | M32 | semidirect |
| 79. C3×C5 | C2×M32 | semidirect |
| 87. C2×C5 | #812 | semidirect |
| 98. C2×C3 | #3944 | semidirect |
| 100. C5 | C2×#812 | semidirect |
| 107. C3 | C2×#3944 | semidirect |
| 109. C2 | #91096 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C5×C8 | 2 |
| #91096 | 2 |
| C2×C3⋊#672 | 2 |
| C2×#3944 | 3 |
| C2×#812 | 5 |