Finite Group DatabasebetaFinite Group DatabasebetaOrder 31424.
228 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 107 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. #30628327 | C2 | semidirect |
| 3. #30628317 | C2 | semidirect |
| 4. #30628316 | C2 | semidirect |
| 5. #30628316 | C2 | semidirect |
| 6. #30628315 | C2 | semidirect |
| 7. #30628302 | C2 | semidirect |
| 10. C4⋊C4×D491 | C2 | semidirect |
| 11. C2×C4⋊C4×C491 | C2 | semidirect |
| 38. C22⋊D491 | Q8 | semidirect |
| 74. C491 | #554 | semidirect |
| 86. C2×C4⋊C4 | D491 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30628336 | 2 |
| #30628327 | 2 |
| #30628317 | 2 |
| #30628316 | 2 |
| #30628315 | 2 |
| #30628302 | 2 |
| C4×C22⋊D491 | 2 |
| C4⋊C4×D491 | 2 |
| C2×C4⋊C4×C491 | 2 |
| #554 | 491 |