Finite Group DatabasebetaFinite Group DatabasebetaOrder 31424.
216 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 95 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. #30628336 | C2 | semidirect |
| 2. #30628332 | C2 | semidirect |
| 3. #30628326 | C2 | semidirect |
| 4. #30628323 | C2 | semidirect |
| 5. #30628319 | C2 | semidirect |
| 6. #30628317 | C2 | semidirect |
| 8. Q8×Dic491 | C2 | semidirect |
| 9. #30628299 | C2 | semidirect |
| 10. #30628296 | C2 | semidirect |
| 11. C22⋊Q8×C491 | C2 | semidirect |
| 73. C491 | #542 | semidirect |
| 81. C22⋊Q8 | D491 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30628336 | 2 |
| #30628332 | 2 |
| #30628326 | 2 |
| #30628323 | 2 |
| #30628319 | 2 |
| #30628317 | 2 |
| #30628311 | 2 |
| Q8×Dic491 | 2 |
| #30628299 | 2 |
| #30628296 | 2 |
| C22⋊Q8×C491 | 2 |
| #542 | 491 |