Finite Group DatabasebetaFinite Group DatabasebetaOrder 31424.
196 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 91 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. #30628335 | C2 | semidirect |
| 3. #30628332 | C2 | semidirect |
| 4. #30628332 | C2 | semidirect |
| 5. #30628330 | C2 | semidirect |
| 6. #30628330 | C2 | semidirect |
| 7. #30628328 | C2 | semidirect |
| 8. #30628327 | C2 | semidirect |
| 12. #30628316 | C2 | semidirect |
| 13. #30628315 | C2 | semidirect |
| 14. #30628313 | C2 | semidirect |
| 15. C22⋊Q8×C491 | C2 | semidirect |
| 97. C491 | #563 | semidirect |
| 113. 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 |
| #30628335 | 2 |
| #30628332 | 2 |
| #30628330 | 2 |
| #30628328 | 2 |
| #30628327 | 2 |
| #30628323 | 2 |
| #30628320 | 2 |
| #30628319 | 2 |
| #30628316 | 2 |
| #30628315 | 2 |
| #30628313 | 2 |
| C22⋊Q8×C491 | 2 |
| #563 | 491 |