Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
376 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 94 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. C3×C5×C22⋊Q8 | C2 | semidirect |
| 3. C2×C3×#688 | C2 | semidirect |
| 4. C3×C22⋊#168 | C2 | semidirect |
| 5. C3×#3941 | C2 | semidirect |
| 6. #65335 | C3 | direct (N × H) |
| 8. C2×C3×C5×Q8 | C22 | semidirect |
| 14. C3×C5×C4⋊C4 | C22 | semidirect |
| 17. C2×C3×#168 | C22 | semidirect |
| 20. C5×C22⋊Q8 | C2×C3 | semidirect |
| 21. C2×#688 | C2×C3 | semidirect |
| 22. C22⋊#168 | C2×C3 | semidirect |
| 23. #3941 | C2×C3 | semidirect |
| 41. C3×C22⋊Q8 | D5 | semidirect |
| 45. C2×C5×Q8 | C22×C3 | semidirect |
| 51. C5×C4⋊C4 | C22×C3 | semidirect |
| 54. C2×#168 | C22×C3 | semidirect |
| 58. C22×C3×C5 | SD16 | semidirect |
| 69. C2×C3×Q8 | C2×D5 | semidirect |
| 77. C3×C4⋊C4 | C2×D5 | semidirect |
| 96. C22⋊Q8 | C3×D5 | semidirect |
| 121. C22×C5 | C3×SD16 | semidirect |
| 132. C2×Q8 | C2×C3×D5 | semidirect |
| 140. C4⋊C4 | C2×C3×D5 | semidirect |
| 142. C3×C5 | #450 | semidirect |
| 149. C22×C3 | #688 | semidirect |
| 180. C5 | C3×#450 | semidirect |
| 187. C22 | C3×#688 | semidirect |
| 193. C3 | #65335 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D20 | 2 |
| C3×C5×C22⋊Q8 | 2 |
| C2×C3×#688 | 2 |
| C3×C22⋊#168 | 2 |
| C3×#3941 | 2 |
| #65335 | 3 |
| C3×#450 | 5 |