Finite Group DatabasebetaFinite Group DatabasebetaOrder 35008.
104 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 37 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. #31776035 | C2 | semidirect |
| 3. C2×#22576765 | C2 | semidirect |
| 4. #31776008 | C2 | semidirect |
| 5. #31775920 | C2 | semidirect |
| 6. #31775918 | C2 | semidirect |
| 7. #108×C547 | C2 | semidirect |
| 51. C547 | #471 | semidirect |
| 57. #108 | D547 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31776035 | 2 |
| #31776030 | 2 |
| C2×#22576765 | 2 |
| #31776008 | 2 |
| #31775920 | 2 |
| #31775918 | 2 |
| #108×C547 | 2 |
| #471 | 547 |