Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
536 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 229 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 |
|---|---|---|
| 4. #14557572 | C2 | direct (N × H) |
| 5. C2×#11924470 | C2 | semidirect |
| 6. C2×#11924469 | C2 | semidirect |
| 7. C2×#11924467 | C2 | semidirect |
| 8. C2×#106×C37 | C2 | semidirect |
| 11. C2×#10596929 | C4 | semidirect |
| 23. #11924470 | C22 | semidirect |
| 24. #11924469 | C22 | semidirect |
| 25. #11924467 | C22 | semidirect |
| 29. #106×C37 | C22 | semidirect |
| 43. C2×C8×C37 | C2×C4 | semidirect |
| 56. C2×#64436 | C2×C4 | semidirect |
| 58. #10596929 | C2×C4 | semidirect |
| 82. C8×C37 | C22×C4 | semidirect |
| 83. #64436 | C22×C4 | semidirect |
| 101. C2×C37 | #428 | semidirect |
| 113. C2×#106 | D37 | semidirect |
| 114. C37 | C2×#428 | semidirect |
| 135. #106 | C2×D37 | semidirect |
| 152. C2×C8 | C4×D37 | semidirect |
| 189. C8 | C2×C4×D37 | semidirect |
| 207. C2 | #14557572 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10596929 | 2 |
| C2×#11924494 | 2 |
| C2×C4⋊C4×D37 | 2 |
| #14557572 | 2 |
| C2×#11924470 | 2 |
| C2×#11924469 | 2 |
| C2×#11924467 | 2 |
| C2×#106×C37 | 2 |
| C2×#428 | 37 |