Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
404 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 122 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×C3⋊#170 | C2 | semidirect |
| 3. C22×C3×#170 | C2 | semidirect |
| 4. #91171 | C2 | direct (N × H) |
| 14. C2×C3⋊#170 | C22 | semidirect |
| 16. C2×C3×#170 | C22 | semidirect |
| 20. C22×#170 | D3 | semidirect |
| 25. C22×D15 | C8 | semidirect |
| 52. C2×#170 | C2×D3 | semidirect |
| 61. C2×D15 | C2×C8 | 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 | #4003 | semidirect |
| 180. C5 | C2×(C2×D3)⋊C8 | semidirect |
| 193. C3 | C2×#4003 | semidirect |
| 195. C2 | #91171 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#1200 | 2 |
| C22×C3⋊#170 | 2 |
| C22×C3×#170 | 2 |
| #91171 | 2 |
| C2×#4003 | 3 |
| C2×(C2×D3)⋊C8 | 5 |