Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
188 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 36 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×#4013 | C2 | semidirect |
| 3. C3×#4011 | C2 | semidirect |
| 4. #64864 | C3 | direct (N × H) |
| 5. C23×C3×D5 | C4 | semidirect |
| 10. C3×C5×C22⋊C4 | C4 | semidirect |
| 14. #4013 | C2×C3 | semidirect |
| 15. #4011 | C2×C3 | semidirect |
| 30. C23×D5 | C3×C4 | semidirect |
| 35. C5×C22⋊C4 | C3×C4 | semidirect |
| 57. C3×C22⋊C4 | AGL(1,𝔽5) | semidirect |
| 107. C22⋊C4 | C3×AGL(1,𝔽5) | semidirect |
| 108. C3×C5 | AΣL(1,𝔽16) | semidirect |
| 143. C5 | C3×AΣL(1,𝔽16) | semidirect |
| 157. C3 | #64864 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4028 | 2 |
| C3×#4013 | 2 |
| C3×#4011 | 2 |
| #64864 | 3 |
| C3×AΣL(1,𝔽16) | 5 |