Finite Group DatabasebetaFinite Group DatabasebetaOrder 31424.
298 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 298 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 |
|---|---|---|
| 1. C2×#21463327 | C2 | semidirect |
| 2. C2×D4×D491 | C2 | semidirect |
| 3. #30628361 | C2 | direct (N × H) |
| 4. C2×#21463317 | C2 | semidirect |
| 5. C2×#21463316 | C2 | semidirect |
| 6. C2×#21463313 | C2 | semidirect |
| 7. C2×#21463311 | C2 | semidirect |
| 8. C2×D8×C491 | C2 | semidirect |
| 11. #21463327 | C22 | semidirect |
| 12. C2×Dic982 | C22 | semidirect |
| 17. D4×D491 | C22 | semidirect |
| 20. #21463317 | C22 | semidirect |
| 21. #21463316 | C22 | semidirect |
| 22. #21463313 | C22 | semidirect |
| 23. #21463311 | C22 | semidirect |
| 24. C2×C491⋊C8 | C22 | semidirect |
| 26. C2×D4×C491 | C22 | semidirect |
| 27. D8×C491 | C22 | semidirect |
| 28. C2×C8×C491 | C22 | semidirect |
| 34. Dic982 | C23 | semidirect |
| 44. C491⋊C8 | C23 | semidirect |
| 50. D4×C491 | C23 | semidirect |
| 52. C8×C491 | C23 | semidirect |
| 69. C2×C491 | AGL(1,ℤ/8) | semidirect |
| 73. C491 | C2×AGL(1,ℤ/8) | semidirect |
| 81. C2×D8 | D491 | semidirect |
| 93. C2×D4 | C2×D491 | semidirect |
| 99. D8 | C2×D491 | semidirect |
| 102. C2×C8 | C2×D491 | semidirect |
| 118. D4 | C22×D491 | semidirect |
| 126. C8 | C22×D491 | semidirect |
| 145. C2 | #30628361 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#21463327 | 2 |
| C2×D4×D491 | 2 |
| #30628361 | 2 |
| C2×#21463317 | 2 |
| C2×#21463316 | 2 |
| C2×#21463313 | 2 |
| C2×#21463311 | 2 |
| C2×D8×C491 | 2 |
| C2×AGL(1,ℤ/8) | 491 |