Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
452 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 158 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. #14558613 | C2 | semidirect |
| 2. #14558579 | C2 | semidirect |
| 3. #14558577 | C2 | semidirect |
| 4. D37⋊#108 | C2 | semidirect |
| 5. #14558532 | C2 | semidirect |
| 6. #14558496 | C2 | semidirect |
| 9. #11924624 | C22 | semidirect |
| 14. #11924607 | C22 | semidirect |
| 15. #11924606 | C22 | semidirect |
| 16. #11924601 | C22 | semidirect |
| 17. #11924590 | C22 | semidirect |
| 18. C8×#3866 | C22 | semidirect |
| 20. #11924559 | C4 | semidirect |
| 21. #11924559 | C4 | semidirect |
| 24. C2×#10596941 | C4 | semidirect |
| 25. C2×D296 | C4 | semidirect |
| 27. C2×Q16×C37 | C4 | semidirect |
| 109. C37 | #2957 | semidirect |
| 115. C2×Q16 | #3866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558613 | 2 |
| #14558579 | 2 |
| #14558577 | 2 |
| D37⋊#108 | 2 |
| #14558532 | 2 |
| #14558496 | 2 |
| C2×#11924559 | 2 |
| #2957 | 37 |