Finite Group DatabasebetaFinite Group DatabasebetaOrder 7040.
892 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 892 conjugacy classes of subgroups — too many to draw. Only its 217 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. #72254541 | C2 | semidirect |
| 2. #72249030 | C2 | semidirect |
| 3. C11⋊C5×#498 | C2 | semidirect |
| 4. C4×#4313⋊C5 | C2 | semidirect |
| 5. #72248922 | C2 | semidirect |
| 6. #72248917 | C2 | semidirect |
| 7. #72248709 | C2 | semidirect |
| 24. #13079355 | C5 | semidirect |
| 45. #10623256 | C2×C5 | semidirect |
| 46. C11×#498 | C2×C5 | semidirect |
| 47. #10622701 | C2×C5 | semidirect |
| 48. #10622482 | C2×C5 | semidirect |
| 49. #10622478 | C2×C5 | semidirect |
| 50. #10622308 | C2×C5 | semidirect |
| 51. C4×#4313 | C2×C5 | semidirect |
| 68. C8×C11⋊C5 | #41 | semidirect |
| 160. C8×C11 | C5×#41 | semidirect |
| 183. #498 | AGL(1,𝔽11) | semidirect |
| 189. C11⋊C5 | #3184 | semidirect |
| 269. C11 | C5×#3184 | semidirect |
| 290. C8 | #4343⋊C5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72254541 | 2 |
| #72249030 | 2 |
| C11⋊C5×#498 | 2 |
| C4×#4313⋊C5 | 2 |
| #72248922 | 2 |
| #72248917 | 2 |
| #72248709 | 2 |
| #13079355 | 5 |
| C5×#3184 | 11 |