Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
544 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 157 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×#10596930 | C2 | semidirect |
| 2. C22×#10596929 | C2 | semidirect |
| 3. C2×#11924516 | C2 | semidirect |
| 5. #14557780 | C2 | direct (N × H) |
| 6. C2×#11924459 | C2 | semidirect |
| 7. C2×#11924456 | C2 | semidirect |
| 8. C2×#107×C37 | C2 | semidirect |
| 14. C2×#10596930 | C22 | semidirect |
| 16. C2×#10596929 | C22 | semidirect |
| 19. #11924516 | C22 | semidirect |
| 25. #11924459 | C22 | semidirect |
| 26. #11924456 | C22 | semidirect |
| 30. #107×C37 | C22 | semidirect |
| 52. C2×C8×C37 | D4 | semidirect |
| 96. C8×C37 | C2×D4 | semidirect |
| 118. C2×C37 | #468 | semidirect |
| 129. C2×#107 | D37 | semidirect |
| 132. C37 | C2×#468 | semidirect |
| 152. #107 | C2×D37 | semidirect |
| 180. C2×C8 | D148 | semidirect |
| 221. C8 | C2×D148 | semidirect |
| 243. C2 | #14557780 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10596930 | 2 |
| C22×#10596929 | 2 |
| C2×#11924516 | 2 |
| C2×#11924511 | 2 |
| #14557780 | 2 |
| C2×#11924459 | 2 |
| C2×#11924456 | 2 |
| C2×#107×C37 | 2 |
| C2×#468 | 37 |