Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
440 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 125 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×D8×D31 | C2 | semidirect |
| 2. C2×D496 | C2 | semidirect |
| 3. C2×#11758414 | C2 | semidirect |
| 4. D16×D31 | C2 | direct (N × H) |
| 5. C2×C16×D31 | C2 | semidirect |
| 6. C2×C31×D16 | C2 | semidirect |
| 8. C2×D8×C31 | C22 | semidirect |
| 11. D8×D31 | C22 | semidirect |
| 12. C2×D248 | C22 | semidirect |
| 14. C31×D16 | C22 | semidirect |
| 15. C2×C16×C31 | C22 | semidirect |
| 16. #11758414 | C22 | semidirect |
| 17. C2×C31⋊C16 | C22 | semidirect |
| 18. D496 | C22 | semidirect |
| 19. C16×D31 | C22 | semidirect |
| 28. D8×C31 | C23 | semidirect |
| 33. D248 | C23 | semidirect |
| 36. C16×C31 | C23 | semidirect |
| 37. C31⋊C16 | C23 | semidirect |
| 62. C2×D31 | D16 | direct (N × H) |
| 71. C2×D16 | D31 | direct (N × H) |
| 74. C2×C31 | C2×D16 | semidirect |
| 77. D31 | C2×D16 | direct (N × H) |
| 83. C2×D8 | C2×D31 | semidirect |
| 87. D16 | C2×D31 | direct (N × H) |
| 90. C2×C16 | C2×D31 | semidirect |
| 91. C31 | C22×D16 | semidirect |
| 103. D8 | C22×D31 | semidirect |
| 109. C16 | C22×D31 | semidirect |
| 141. C2 | D16×D31 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D31 | 2 |
| C2×D496 | 2 |
| C2×#11758414 | 2 |
| D16×D31 | 2 |
| C2×C16×D31 | 2 |
| C2×C31×D16 | 2 |
| C22×D16 | 31 |