Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
376 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 76 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. C5×#924 | C2 | semidirect |
| 3. C2×#6660 | C2 | semidirect |
| 4. C3×C22⋊#168 | C2 | semidirect |
| 5. #90969 | C2 | semidirect |
| 12. C2×C5×Dic6 | C22 | semidirect |
| 14. C5×C4⋊Dic3 | C22 | semidirect |
| 16. C2×C3×#168 | C22 | semidirect |
| 22. C22⋊#168 | D3 | semidirect |
| 40. #924 | D5 | semidirect |
| 54. C2×#168 | C2×D3 | semidirect |
| 58. C22×C3×C5 | SD16 | semidirect |
| 73. C2×Dic6 | C2×D5 | semidirect |
| 76. C4⋊Dic3 | C2×D5 | semidirect |
| 121. C22×C5 | #204 | semidirect |
| 142. C3×C5 | #450 | semidirect |
| 145. C22×C3 | #688 | semidirect |
| 180. C5 | #4731 | semidirect |
| 187. C22 | #6660 | semidirect |
| 193. C3 | #65335 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D60 | 2 |
| C5×#924 | 2 |
| C2×#6660 | 2 |
| C3×C22⋊#168 | 2 |
| #90969 | 2 |
| #65335 | 3 |
| #4731 | 5 |