Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
524 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 524 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 |
|---|---|---|
| 1. C22×D296 | C2 | semidirect |
| 2. C2×#11924542 | C2 | semidirect |
| 3. #14558102 | C2 | semidirect |
| 4. #14557787 | C2 | semidirect |
| 5. #14557770 | C2 | semidirect |
| 6. #14557537 | C2 | semidirect |
| 7. C37×#427 | C2 | semidirect |
| 15. C2×#10596929 | C22 | semidirect |
| 16. C2×C8×D37 | C22 | semidirect |
| 19. #11924511 | C22 | semidirect |
| 21. #11924456 | C22 | semidirect |
| 24. #107×C37 | C22 | semidirect |
| 25. #106×C37 | C22 | semidirect |
| 39. C2×C8×C37 | D4 | semidirect |
| 99. #427 | D37 | semidirect |
| 101. C37 | #3058 | semidirect |
| 117. #107 | C2×D37 | semidirect |
| 118. #106 | C2×D37 | semidirect |
| 139. C2×C8 | D148 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D296 | 2 |
| C2×#11924542 | 2 |
| #14558102 | 2 |
| #14557787 | 2 |
| #14557770 | 2 |
| #14557537 | 2 |
| C37×#427 | 2 |
| #3058 | 37 |