Finite Group DatabasebetaFinite Group DatabasebetaOrder 3520.
204 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 90 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. #108×C11⋊C5 | C2 | semidirect |
| 4. #66886⋊C5 | C2 | semidirect |
| 5. #66883⋊C5 | C2 | semidirect |
| 14. #10622506 | C5 | semidirect |
| 26. C11×#108 | C2×C5 | semidirect |
| 27. #66886 | C2×C5 | semidirect |
| 28. #66883 | C2×C5 | semidirect |
| 70. C11⋊C5 | #430 | semidirect |
| 90. #108 | AGL(1,𝔽11) | semidirect |
| 108. C11 | C5×#430 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| M16×AGL(1,𝔽11) | 2 |
| C2×#4313⋊C5 | 2 |
| #108×C11⋊C5 | 2 |
| #66886⋊C5 | 2 |
| #66883⋊C5 | 2 |
| #10622506 | 5 |
| C5×#430 | 11 |