Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 133 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. #14558090 | C2 | semidirect |
| 3. #14557893 | C2 | semidirect |
| 4. #14557888 | C2 | semidirect |
| 5. #14557543 | C2 | semidirect |
| 7. C4×M16×C37 | C2 | semidirect |
| 10. #11924536 | C22 | semidirect |
| 11. #11924528 | C22 | semidirect |
| 19. #11924461 | C22 | semidirect |
| 23. #97×C37 | C22 | semidirect |
| 24. C4×C8×C37 | C22 | semidirect |
| 90. C4×M16 | D37 | semidirect |
| 91. C37 | #3140 | semidirect |
| 107. #97 | C2×D37 | semidirect |
| 108. C4×C8 | C2×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558090 | 2 |
| C2×#11924524 | 2 |
| #14557893 | 2 |
| #14557888 | 2 |
| #14557543 | 2 |
| #14557539 | 2 |
| C4×M16×C37 | 2 |
| #3140 | 37 |