Finite Group DatabasebetaFinite Group DatabasebetaOrder 31424.
234 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 103 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. #30628331 | C2 | semidirect |
| 2. #30628329 | C2 | semidirect |
| 3. #30628325 | C2 | semidirect |
| 4. #30628320 | C2 | semidirect |
| 5. #30628316 | C2 | semidirect |
| 7. C4×Dic982 | C2 | semidirect |
| 8. C4×D1964 | C2 | semidirect |
| 9. C4×C22⋊D491 | C2 | semidirect |
| 10. #30628294 | C2 | semidirect |
| 11. C2×C42×C491 | C2 | semidirect |
| 74. C491 | #529 | semidirect |
| 86. C2×C42 | D491 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30628331 | 2 |
| #30628329 | 2 |
| #30628325 | 2 |
| #30628320 | 2 |
| #30628316 | 2 |
| #30628311 | 2 |
| C4×Dic982 | 2 |
| C4×D1964 | 2 |
| C4×C22⋊D491 | 2 |
| #30628294 | 2 |
| C2×C42×C491 | 2 |
| #529 | 491 |