Finite Group DatabasebetaFinite Group DatabasebetaOrder 3520.
288 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|---|
| 1. #127×C11⋊C5 | C2 | semidirect |
| 2. C2×#4324⋊C5 | C2 | semidirect |
| 3. C2×#4323⋊C5 | C2 | semidirect |
| 4. #66928⋊C5 | C2 | semidirect |
| 5. #66867⋊C5 | C2 | semidirect |
| 15. #10622687 | C5 | semidirect |
| 26. (C11⋊C5)⋊C8 | D4 | semidirect |
| 27. C11×#127 | C2×C5 | semidirect |
| 28. C2×#4324 | C2×C5 | semidirect |
| 29. C2×#4323 | C2×C5 | semidirect |
| 30. #66928 | C2×C5 | semidirect |
| 31. #66867 | C2×C5 | semidirect |
| 69. C11⋊C8 | C5×D4 | semidirect |
| 80. C11⋊C5 | #496 | semidirect |
| 102. #127 | AGL(1,𝔽11) | semidirect |
| 126. C11 | C5×#496 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #127×C11⋊C5 | 2 |
| C2×#4324⋊C5 | 2 |
| C2×#4323⋊C5 | 2 |
| #66928⋊C5 | 2 |
| #66867⋊C5 | 2 |
| #10622687 | 5 |
| C5×#496 | 11 |