Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
458 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 185 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. #14558299 | C2 | semidirect |
| 3. #14557656 | C2 | semidirect |
| 4. #14557651 | C2 | semidirect |
| 5. #14557582 | C2 | semidirect |
| 6. C2×#11924464 | C2 | semidirect |
| 7. C4×M16×C37 | C2 | semidirect |
| 9. #11924569 | C4 | semidirect |
| 10. #11924564 | C4 | semidirect |
| 13. #11924542 | C22 | semidirect |
| 16. #11924472 | C22 | semidirect |
| 17. #11924464 | C22 | semidirect |
| 18. #11924464 | C22 | semidirect |
| 22. #97×C37 | C22 | semidirect |
| 23. C4×C8×C37 | C22 | semidirect |
| 44. Dic148 | C2×C4 | semidirect |
| 45. D296 | C2×C4 | semidirect |
| 46. #10596930 | C2×C4 | semidirect |
| 92. C4×M16 | D37 | semidirect |
| 93. C37 | #2956 | semidirect |
| 108. #97 | C2×D37 | semidirect |
| 109. C4×C8 | C2×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558333 | 2 |
| #14558299 | 2 |
| #14557656 | 2 |
| #14557651 | 2 |
| #14557582 | 2 |
| C2×#11924464 | 2 |
| C4×M16×C37 | 2 |
| #2956 | 37 |