Finite Group DatabasebetaFinite Group DatabasebetaOrder 31424.
270 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 270 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 |
|---|---|---|
| 2. C2×Q8×D491 | C2 | semidirect |
| 3. #30628336 | C2 | semidirect |
| 4. #30628323 | C2 | semidirect |
| 5. #30628322 | C2 | semidirect |
| 6. #30628319 | C2 | semidirect |
| 7. #30628317 | C2 | semidirect |
| 8. #30628316 | C2 | semidirect |
| 9. #30628313 | C2 | semidirect |
| 10. #30628295 | C2 | semidirect |
| 11. C22⋊Q8×C491 | C2 | semidirect |
| 83. C491 | #536 | semidirect |
| 94. C22⋊Q8 | D491 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#21463328 | 2 |
| C2×Q8×D491 | 2 |
| #30628336 | 2 |
| #30628323 | 2 |
| #30628322 | 2 |
| #30628319 | 2 |
| #30628317 | 2 |
| #30628316 | 2 |
| #30628313 | 2 |
| #30628295 | 2 |
| C22⋊Q8×C491 | 2 |
| #536 | 491 |