Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
404 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 144 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. C22×C5×C3⋊C8 | C2 | semidirect |
| 3. C22×C3×#168 | C2 | semidirect |
| 4. #90957 | C2 | direct (N × H) |
| 14. C2×C5×C3⋊C8 | C22 | semidirect |
| 16. C2×C3×#168 | C22 | semidirect |
| 20. C22×#168 | D3 | semidirect |
| 25. C22×D15 | C8 | semidirect |
| 40. C22×C3⋊C8 | D5 | semidirect |
| 52. C2×#168 | C2×D3 | semidirect |
| 61. C2×D15 | C2×C8 | semidirect |
| 76. C2×C3⋊C8 | C2×D5 | semidirect |
| 97. C2×C3×C5 | C22⋊C8 | semidirect |
| 141. C3×C5 | C2×C22⋊C8 | semidirect |
| 154. C2×C5 | (C2×D3)⋊C8 | semidirect |
| 175. C2×C3 | #3952 | semidirect |
| 180. C5 | C2×(C2×D3)⋊C8 | semidirect |
| 193. C3 | C2×#3952 | semidirect |
| 195. C2 | #90957 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D15 | 2 |
| C22×C5×C3⋊C8 | 2 |
| C22×C3×#168 | 2 |
| #90957 | 2 |
| C2×#3952 | 3 |
| C2×(C2×D3)⋊C8 | 5 |