Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
516 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 168 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. #14558482 | C2 | semidirect |
| 3. #14558478 | C2 | semidirect |
| 4. C4⋊C4×#3866 | C2 | semidirect |
| 6. C42×#3866 | C2 | semidirect |
| 18. #11924531 | C4 | semidirect |
| 19. #11924530 | C4 | semidirect |
| 20. #11924529 | C4 | semidirect |
| 24. #126×C37 | C4 | semidirect |
| 38. C4⋊C4×C37 | C2×C4 | semidirect |
| 40. C42×C37 | C2×C4 | semidirect |
| 44. C4⋊Dic37 | C2×C4 | semidirect |
| 45. #10596936 | C2×C4 | semidirect |
| 46. #10596936 | C2×C4 | semidirect |
| 47. C4×Dic37 | C2×C4 | semidirect |
| 80. #3866 | #126 | direct (N × H) |
| 98. C37 | C4×#126 | semidirect |
| 103. #126 | #3866 | direct (N × H) |
| 128. C4⋊C4 | C2×#3866 | semidirect |
| 138. C42 | C2×#3866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558483 | 2 |
| #14558482 | 2 |
| #14558478 | 2 |
| C4⋊C4×#3866 | 2 |
| C22⋊C4×#3866 | 2 |
| C42×#3866 | 2 |
| #126×D37 | 2 |
| C4×#126 | 37 |