Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 564 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. C22×#10596942 | C2 | semidirect |
| 4. C2×#11924534 | C2 | semidirect |
| 6. #14557926 | C2 | direct (N × H) |
| 7. C2×#11924446 | C2 | semidirect |
| 8. C22×Q16×C37 | C2 | semidirect |
| 12. C2×#10596942 | C22 | semidirect |
| 19. #11924534 | C22 | semidirect |
| 25. #11924446 | C22 | semidirect |
| 29. C2×Q16×C37 | C22 | semidirect |
| 109. C2×C37 | #497 | semidirect |
| 114. C22×Q16 | D37 | semidirect |
| 121. C37 | C2×#497 | semidirect |
| 129. C2×Q16 | C2×D37 | semidirect |
| 222. C2 | #14557926 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10596942 | 2 |
| C22×#10596930 | 2 |
| C22×#10596941 | 2 |
| C2×#11924534 | 2 |
| C2×#11924525 | 2 |
| #14557926 | 2 |
| C2×#11924446 | 2 |
| C22×Q16×C37 | 2 |
| C2×#497 | 37 |