Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
228 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 3. C3×#3994 | C2 | semidirect |
| 4. C3×#3993 | C2 | semidirect |
| 5. #65721 | C3 | direct (N × H) |
| 10. C2×C3×C5×C8 | C4 | semidirect |
| 11. C2×C3×#168 | C4 | semidirect |
| 12. C3×C8×D5 | C4 | semidirect |
| 13. C3×C8×D5 | C4 | semidirect |
| 19. #3994 | C2×C3 | semidirect |
| 20. #3993 | C2×C3 | semidirect |
| 41. C2×C5×C8 | C3×C4 | semidirect |
| 42. C2×#168 | C3×C4 | semidirect |
| 43. C8×D5 | C3×C4 | semidirect |
| 44. C8×D5 | C3×C4 | semidirect |
| 63. C2×C3×C8 | AGL(1,𝔽5) | semidirect |
| 114. C2×C8 | C3×AGL(1,𝔽5) | semidirect |
| 118. C3×C5 | #427 | semidirect |
| 148. C5 | C3×#427 | semidirect |
| 158. C3 | #65721 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4130 | 2 |
| C2×C3×C8×D5 | 2 |
| C3×#3994 | 2 |
| C3×#3993 | 2 |
| #65721 | 3 |
| C3×#427 | 5 |