Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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. #14557830 | C2 | semidirect |
| 3. #14557830 | C2 | semidirect |
| 4. #14557820 | C2 | semidirect |
| 5. #14557810 | C2 | semidirect |
| 6. #14557573 | C2 | semidirect |
| 7. #14557569 | C2 | semidirect |
| 8. #14557560 | C2 | semidirect |
| 11. C37×#544 | C2 | semidirect |
| 21. #11924469 | C22 | semidirect |
| 22. #11924469 | C22 | semidirect |
| 23. #11924469 | C22 | semidirect |
| 24. #11924467 | C22 | semidirect |
| 25. #11924467 | C22 | semidirect |
| 26. #11924467 | C22 | semidirect |
| 27. C4⋊#64436 | C22 | semidirect |
| 28. C4⋊#64436 | C22 | semidirect |
| 34. C4⋊Q8×C37 | C22 | semidirect |
| 36. #125×C37 | C22 | semidirect |
| 47. C2×D148 | Q8 | semidirect |
| 125. #544 | D37 | semidirect |
| 136. C37 | #3081 | semidirect |
| 141. C4⋊Q8 | C2×D37 | semidirect |
| 143. #125 | C2×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558007 | 2 |
| #14557830 | 2 |
| #14557820 | 2 |
| #14557810 | 2 |
| #14557573 | 2 |
| #14557569 | 2 |
| #14557560 | 2 |
| #14557537 | 2 |
| C2×#11924456 | 2 |
| C37×#544 | 2 |
| #3081 | 37 |