Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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. C2×#11924544 | C2 | semidirect |
| 2. C22×#10596929 | C2 | semidirect |
| 4. #14557610 | C2 | semidirect |
| 5. #14557603 | C2 | semidirect |
| 6. #14557499 | C2 | semidirect |
| 7. #14557496 | C2 | semidirect |
| 8. #14557489 | C2 | semidirect |
| 9. C37×#424 | C2 | semidirect |
| 17. C2×#10596929 | C22 | semidirect |
| 19. C2×C8×D37 | C22 | semidirect |
| 26. #11924448 | C22 | semidirect |
| 27. #11924447 | C22 | semidirect |
| 28. C4×#64436 | C22 | semidirect |
| 32. C4⋊C8×C37 | C22 | semidirect |
| 58. C2×#64436 | D4 | semidirect |
| 119. #424 | D37 | semidirect |
| 123. C37 | #2930 | semidirect |
| 142. C4⋊C8 | C2×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924544 | 2 |
| C22×#10596929 | 2 |
| #14558045 | 2 |
| #14557610 | 2 |
| #14557603 | 2 |
| #14557499 | 2 |
| #14557496 | 2 |
| #14557489 | 2 |
| C37×#424 | 2 |
| #2930 | 37 |