Finite Group DatabasebetaFinite Group DatabasebetaOrder 31424.
106 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 45 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 |
|---|---|---|
| 2. #30628345 | C2 | semidirect |
| 3. #30628344 | C2 | semidirect |
| 4. #30628272 | C2 | semidirect |
| 5. #30628265 | C2 | semidirect |
| 6. C4×C491⋊C8 | C2 | semidirect |
| 7. #104×C491 | C2 | semidirect |
| 9. #21463318 | C4 | semidirect |
| 10. #21463316 | C4 | semidirect |
| 11. #21463315 | C4 | semidirect |
| 12. #21463313 | C4 | semidirect |
| 51. C491 | #443 | semidirect |
| 58. #104 | D491 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30628357 | 2 |
| #30628345 | 2 |
| #30628344 | 2 |
| #30628272 | 2 |
| #30628265 | 2 |
| C4×C491⋊C8 | 2 |
| #104×C491 | 2 |
| #443 | 491 |