Finite Group DatabasebetaFinite Group DatabasebetaOrder 3520.
288 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 76 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. C2×D88⋊C5 | C2 | semidirect |
| 2. C2×#4314⋊C5 | C2 | semidirect |
| 3. #66928⋊C5 | C2 | semidirect |
| 4. #66927⋊C5 | C2 | semidirect |
| 5. #97×C11⋊C5 | C2 | semidirect |
| 15. #10622325 | C5 | semidirect |
| 26. C8×C11⋊C5 | D4 | semidirect |
| 27. C2×D88 | C2×C5 | semidirect |
| 28. C2×#4314 | C2×C5 | semidirect |
| 29. #66928 | C2×C5 | semidirect |
| 30. #66927 | C2×C5 | semidirect |
| 31. C11×#97 | C2×C5 | semidirect |
| 69. C8×C11 | C5×D4 | semidirect |
| 80. C11⋊C5 | #496 | semidirect |
| 104. #97 | AGL(1,𝔽11) | semidirect |
| 126. C11 | C5×#496 | semidirect |
| 141. C8 | 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×D88⋊C5 | 2 |
| C2×#4314⋊C5 | 2 |
| #66928⋊C5 | 2 |
| #66927⋊C5 | 2 |
| #97×C11⋊C5 | 2 |
| #10622325 | 5 |
| C5×#496 | 11 |