Finite Group DatabasebetaFinite Group DatabasebetaOrder 31424.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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. #30628332 | C2 | semidirect |
| 2. #30628330 | C2 | semidirect |
| 3. #30628327 | C2 | semidirect |
| 4. #30628323 | C2 | semidirect |
| 5. #30628321 | C2 | semidirect |
| 6. #30628318 | C2 | semidirect |
| 7. #30628314 | C2 | semidirect |
| 9. C4×Dic982 | C2 | semidirect |
| 10. C4×C22⋊D491 | C2 | semidirect |
| 11. C4×C22⋊D491 | C2 | semidirect |
| 12. #30628296 | C2 | semidirect |
| 13. #30628294 | C2 | semidirect |
| 14. C2×C4×Dic491 | C2 | semidirect |
| 15. C4×D4×C491 | C2 | semidirect |
| 103. C491 | #529 | semidirect |
| 116. C4×D4 | D491 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30628332 | 2 |
| #30628330 | 2 |
| #30628327 | 2 |
| #30628323 | 2 |
| #30628321 | 2 |
| #30628318 | 2 |
| #30628314 | 2 |
| #30628309 | 2 |
| C4×Dic982 | 2 |
| C4×C22⋊D491 | 2 |
| #30628296 | 2 |
| #30628294 | 2 |
| C2×C4×Dic491 | 2 |
| C4×D4×C491 | 2 |
| #529 | 491 |