Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
244 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 62 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. ΓL(1,𝔽16)⋊Q8 | C2 | semidirect |
| 4. C8×ΓL(1,𝔽16) | C2 | semidirect |
| 5. C3×#3993 | C2 | semidirect |
| 6. #91153 | C2 | semidirect |
| 19. #6706 | C4 | semidirect |
| 20. C5×#204 | C4 | semidirect |
| 22. #6660 | C4 | semidirect |
| 23. #6659 | C4 | semidirect |
| 30. #3993 | D3 | semidirect |
| 39. Dic30 | C2×C4 | semidirect |
| 41. C5×Dic6 | C2×C4 | semidirect |
| 47. C3×C5×C8 | C2×C4 | semidirect |
| 48. C3×#168 | C2×C4 | semidirect |
| 78. ΓL(1,𝔽16) | SD16 | semidirect |
| 99. #204 | AGL(1,𝔽5) | semidirect |
| 115. C5×C8 | C4×D3 | semidirect |
| 116. #168 | C4×D3 | semidirect |
| 142. Dic6 | C2×AGL(1,𝔽5) | semidirect |
| 144. C3×C8 | C2×AGL(1,𝔽5) | semidirect |
| 174. C3×C5 | C4×SD16 | semidirect |
| 209. C8 | D3×AGL(1,𝔽5) | semidirect |
| 215. C5 | #4852 | semidirect |
| 229. C3 | SD16×AGL(1,𝔽5) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #91921 | 2 |
| ΓL(1,𝔽16)⋊Q8 | 2 |
| D5×#204 | 2 |
| C8×ΓL(1,𝔽16) | 2 |
| C3×#3993 | 2 |
| #91153 | 2 |
| #91151 | 2 |
| SD16×AGL(1,𝔽5) | 3 |
| #4852 | 5 |