Finite Group DatabasebetaFinite Group DatabasebetaOrder 3240.
172 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 172 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. #13108184 | C2 | semidirect |
| 3. AGL(1,𝔽5)×#731 | C2 | semidirect |
| 6. C5⋊#4176 | C4 | semidirect |
| 7. C5×#4176 | C4 | semidirect |
| 16. C3×C9×AGL(1,𝔽5) | D3 | semidirect |
| 17. C5×#731 | C2×C4 | semidirect |
| 45. #4176 | AGL(1,𝔽5) | direct (N × H) |
| 48. C3×C5×C9 | C4×D3 | semidirect |
| 69. #731 | C2×AGL(1,𝔽5) | semidirect |
| 115. C3×C9 | D3×AGL(1,𝔽5) | semidirect |
| 121. AGL(1,𝔽5) | #4176 | direct (N × H) |
| 161. C5 | C4×#4176 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#4176 | 2 |
| #13108184 | 2 |
| AGL(1,𝔽5)×#731 | 2 |
| AGL(1,𝔽5)×#272 | 3 |
| D3×C9×AGL(1,𝔽5) | 3 |
| C4×#4176 | 5 |