Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
816 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 269 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. C22×C4⋊Dic37 | C2 | semidirect |
| 3. #14557535 | C2 | direct (N × H) |
| 4. C2×#11924461 | C2 | semidirect |
| 5. C2×#11924458 | C2 | semidirect |
| 6. C22×M16×C37 | C2 | semidirect |
| 9. C2×#10596962 | C4 | semidirect |
| 19. C2×C4⋊Dic37 | C22 | semidirect |
| 20. #11924461 | C22 | semidirect |
| 21. #11924458 | C22 | semidirect |
| 24. C2×M16×C37 | C22 | semidirect |
| 42. #10596962 | C2×C4 | semidirect |
| 45. C2×D148 | C2×C4 | semidirect |
| 51. C2×Dic74 | C2×C4 | semidirect |
| 85. D148 | C22×C4 | semidirect |
| 89. Dic74 | C22×C4 | semidirect |
| 111. C2×C37 | #417 | semidirect |
| 117. C22×M16 | D37 | semidirect |
| 122. C37 | C2×#417 | semidirect |
| 134. C2×M16 | C2×D37 | semidirect |
| 227. C2 | #14557535 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10596962 | 2 |
| C22×C4⋊Dic37 | 2 |
| #14557535 | 2 |
| C2×#11924461 | 2 |
| C2×#11924458 | 2 |
| C22×M16×C37 | 2 |
| C2×#417 | 37 |