Finite Group DatabasebetaFinite Group DatabasebetaOrder 31424.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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. #30628332 | C2 | semidirect |
| 2. #30628328 | C2 | semidirect |
| 3. #30628326 | C2 | semidirect |
| 4. #30628322 | C2 | semidirect |
| 5. #30628313 | C2 | semidirect |
| 7. C4×D1964 | C2 | semidirect |
| 8. C4×D1964 | C2 | semidirect |
| 9. #30628294 | C2 | semidirect |
| 10. C42×D491 | C2 | semidirect |
| 11. C4×Q8×C491 | C2 | semidirect |
| 74. C491 | #529 | semidirect |
| 82. C4×Q8 | D491 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30628332 | 2 |
| #30628328 | 2 |
| #30628326 | 2 |
| #30628322 | 2 |
| #30628313 | 2 |
| #30628312 | 2 |
| C4×D1964 | 2 |
| #30628294 | 2 |
| C42×D491 | 2 |
| C4×Q8×C491 | 2 |
| #529 | 491 |