Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
760 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 165 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×D37 | C2 | semidirect |
| 2. #127×D37 | C2 | semidirect |
| 3. #14557910 | C2 | semidirect |
| 4. #14557909 | C2 | semidirect |
| 5. #14557908 | C2 | semidirect |
| 6. C4×C8×D37 | C2 | semidirect |
| 7. C37×#493 | C2 | semidirect |
| 10. C2×D296 | C22 | semidirect |
| 11. C2×#10596939 | C22 | semidirect |
| 14. #11924533 | C22 | semidirect |
| 16. #11924532 | C22 | semidirect |
| 18. C4×#64436 | C22 | semidirect |
| 19. C8×Dic37 | C22 | semidirect |
| 20. C2×D8×C37 | C22 | semidirect |
| 21. #127×C37 | C22 | semidirect |
| 22. C4×C8×C37 | C22 | semidirect |
| 42. C8×D37 | D4 | semidirect |
| 58. C4×D37 | D8 | semidirect |
| 60. C8×C37 | C2×D4 | semidirect |
| 61. #64436 | C2×D4 | semidirect |
| 70. C4×C37 | C2×D8 | semidirect |
| 73. Dic37 | C2×D8 | semidirect |
| 79. D37 | #493 | direct (N × H) |
| 85. #493 | D37 | direct (N × H) |
| 87. C37 | C2×#493 | semidirect |
| 93. C2×D8 | C2×D37 | semidirect |
| 98. #127 | C2×D37 | semidirect |
| 102. C4×C8 | C2×D37 | semidirect |
| 141. C8 | D4×D37 | semidirect |
| 152. C4 | D8×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D37 | 2 |
| #127×D37 | 2 |
| #14557910 | 2 |
| #14557909 | 2 |
| #14557908 | 2 |
| C4×C8×D37 | 2 |
| C37×#493 | 2 |
| C2×#493 | 37 |