Finite Group DatabasebetaFinite Group DatabasebetaOrder 31424.
170 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 53 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. M16×D491 | C2 | semidirect |
| 3. C42×D491 | C2 | semidirect |
| 4. #30628265 | C2 | semidirect |
| 5. #30628264 | C2 | semidirect |
| 6. #30628263 | C2 | semidirect |
| 7. #104×C491 | C2 | semidirect |
| 8. #21463329 | C4 | semidirect |
| 12. #21463327 | C4 | semidirect |
| 13. Q8×D491 | C4 | semidirect |
| 15. D4×D491 | C4 | semidirect |
| 19. #21463312 | C22 | semidirect |
| 23. C4×Dic491 | C22 | semidirect |
| 25. M16×C491 | C22 | semidirect |
| 26. C42×C491 | C22 | semidirect |
| 30. Dic982 | C2×C4 | semidirect |
| 32. D1964 | C2×C4 | semidirect |
| 48. Q8×C491 | C2×C4 | semidirect |
| 50. D4×C491 | C2×C4 | semidirect |
| 75. D491 | #104 | direct (N × H) |
| 76. C491 | C2×#104 | semidirect |
| 84. #104 | D491 | direct (N × H) |
| 99. M16 | C2×D491 | semidirect |
| 103. C42 | C2×D491 | semidirect |
| 108. Q8 | C4×D491 | semidirect |
| 115. D4 | C4×D491 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×D491 | 2 |
| M16×D491 | 2 |
| C42×D491 | 2 |
| #30628265 | 2 |
| #30628264 | 2 |
| #30628263 | 2 |
| #104×C491 | 2 |
| C2×#104 | 491 |