Finite Group DatabasebetaFinite Group DatabasebetaOrder 31424.
228 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 105 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. #30628335 | C2 | semidirect |
| 2. #30628327 | C2 | semidirect |
| 3. #30628327 | C2 | semidirect |
| 4. #30628315 | C2 | semidirect |
| 5. #30628315 | C2 | semidirect |
| 6. #30628314 | C2 | semidirect |
| 7. #30628314 | C2 | semidirect |
| 8. #30628313 | C2 | semidirect |
| 9. #30628302 | C2 | semidirect |
| 13. C2×Dic491⋊C4 | C2 | semidirect |
| 14. C4⋊C4×D491 | C2 | semidirect |
| 15. C22⋊Q8×C491 | C2 | semidirect |
| 54. C22⋊D491 | Q8 | semidirect |
| 101. C491 | #554 | semidirect |
| 111. C22⋊Q8 | D491 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30628335 | 2 |
| #30628327 | 2 |
| #30628315 | 2 |
| #30628314 | 2 |
| #30628313 | 2 |
| #30628302 | 2 |
| C4×C22⋊D491 | 2 |
| (C22⋊D491)⋊C4 | 2 |
| C2×Dic491⋊C4 | 2 |
| C4⋊C4×D491 | 2 |
| C22⋊Q8×C491 | 2 |
| #554 | 491 |