Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
184 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 87 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. C4⋊C4×C11⋊C5 | C2 | semidirect |
| 4. C4⋊(Dic11⋊C5) | C2 | semidirect |
| 5. (Dic11⋊C4)⋊C5 | C2 | semidirect |
| 12. C4×AGL(1,𝔽11) | C4 | semidirect |
| 13. C4⋊C4×D11 | C5 | semidirect |
| 19. C4×C11⋊C5 | C2×C4 | semidirect |
| 21. Dic11⋊C5 | C2×C4 | semidirect |
| 24. C11×C4⋊C4 | C2×C5 | semidirect |
| 25. C4⋊Dic11 | C2×C5 | semidirect |
| 26. Dic11⋊C4 | C2×C5 | semidirect |
| 31. AGL(1,𝔽11) | C4⋊C4 | direct (N × H) |
| 38. C4×D11 | C4×C5 | semidirect |
| 44. C11⋊C5 | C2×C4⋊C4 | semidirect |
| 50. C4×C11 | C2×C4×C5 | semidirect |
| 52. Dic11 | C2×C4×C5 | semidirect |
| 64. D11 | C5×C4⋊C4 | semidirect |
| 77. C4⋊C4 | AGL(1,𝔽11) | direct (N × H) |
| 78. C11 | C2×C5×C4⋊C4 | semidirect |
| 98. C4 | C4×AGL(1,𝔽11) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×AGL(1,𝔽11) | 2 |
| C4⋊C4×C11⋊C5 | 2 |
| C4⋊(Dic11⋊C5) | 2 |
| (Dic11⋊C4)⋊C5 | 2 |
| C4⋊C4×D11 | 5 |
| C2×C5×C4⋊C4 | 11 |