Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
208 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 56 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 |
|---|---|---|
| 1. #91992 | C2 | semidirect |
| 2. #91916 | C2 | semidirect |
| 4. C3×#4010 | C2 | semidirect |
| 5. #91161 | C2 | semidirect |
| 6. #91158 | C2 | semidirect |
| 7. #91149 | C2 | semidirect |
| 19. #6717 | C4 | semidirect |
| 20. C5×#216 | C4 | semidirect |
| 21. #6655 | C4 | semidirect |
| 22. #6653 | C4 | semidirect |
| 29. #4010 | D3 | semidirect |
| 83. #216 | AGL(1,𝔽5) | semidirect |
| 160. C3×C5 | #444 | semidirect |
| 193. C5 | #4823 | semidirect |
| 202. C3 | #65741 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #91992 | 2 |
| #91916 | 2 |
| #91516 | 2 |
| C3×#4010 | 2 |
| #91161 | 2 |
| #91158 | 2 |
| #91149 | 2 |
| #65741 | 3 |
| #4823 | 5 |