Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
308 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 96 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×#4130 | C2 | semidirect |
| 3. C3×D5⋊M16 | C2 | semidirect |
| 4. C3×#4010 | C2 | semidirect |
| 5. #65784 | C3 | direct (N × H) |
| 6. C2×C3×C5×Q8 | C4 | semidirect |
| 9. C3×#713 | C4 | semidirect |
| 12. C2×C3×D20 | C4 | semidirect |
| 18. C3×C4×AGL(1,𝔽5) | C22 | semidirect |
| 19. C3×#700 | C22 | semidirect |
| 23. #4130 | C2×C3 | semidirect |
| 24. D5⋊M16 | C2×C3 | semidirect |
| 25. #4010 | C2×C3 | semidirect |
| 49. C2×C5×Q8 | C3×C4 | semidirect |
| 52. #713 | C3×C4 | semidirect |
| 55. C2×D20 | C3×C4 | semidirect |
| 61. C4×AGL(1,𝔽5) | C22×C3 | semidirect |
| 62. #700 | C22×C3 | semidirect |
| 81. C2×C3×Q8 | AGL(1,𝔽5) | semidirect |
| 155. C2×Q8 | C3×AGL(1,𝔽5) | semidirect |
| 166. C3×C5 | #421 | semidirect |
| 208. C5 | C3×#421 | semidirect |
| 221. C3 | #65784 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#713 | 2 |
| C3×#4130 | 2 |
| C3×D5⋊M16 | 2 |
| C3×#4010 | 2 |
| #65784 | 3 |
| C3×#421 | 5 |