Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
608 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 237 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×D4×Dic37 | C2 | semidirect |
| 2. #14557645 | C2 | direct (N × H) |
| 3. C2×#11924468 | C2 | semidirect |
| 4. C2×#11924457 | C2 | semidirect |
| 5. C2×#11924446 | C2 | semidirect |
| 10. D4×Dic37 | C22 | semidirect |
| 14. #11924468 | C22 | semidirect |
| 15. #11924457 | C22 | semidirect |
| 16. #11924446 | C22 | semidirect |
| 18. C2×D8×C37 | C4 | semidirect |
| 24. C2×D4×C37 | C2×C4 | semidirect |
| 31. D8×C37 | C2×C4 | semidirect |
| 32. C2×C8×C37 | C2×C4 | semidirect |
| 48. D4×C37 | C22×C4 | semidirect |
| 58. C8×C37 | C22×C4 | semidirect |
| 74. C2×C37 | #442 | semidirect |
| 83. C37 | C2×#442 | semidirect |
| 86. C2×D8 | Dic37 | semidirect |
| 101. C2×D4 | C2×Dic37 | semidirect |
| 108. D8 | C2×Dic37 | semidirect |
| 111. C2×C8 | C2×Dic37 | semidirect |
| 125. D4 | C22×Dic37 | semidirect |
| 136. C8 | C22×Dic37 | semidirect |
| 150. C2 | #14557645 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×Dic37 | 2 |
| #14557645 | 2 |
| C2×#11924468 | 2 |
| C2×#11924457 | 2 |
| C2×#11924446 | 2 |
| C22×D8×C37 | 2 |
| C2×#442 | 37 |