Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
392 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 173 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. #14557595 | C2 | semidirect |
| 3. #14557592 | C2 | semidirect |
| 4. #14557556 | C2 | semidirect |
| 6. C4×#10596934 | C2 | semidirect |
| 7. C4×M16×C37 | C2 | semidirect |
| 16. #11924465 | C22 | semidirect |
| 18. #11924447 | C22 | semidirect |
| 19. C4×#64436 | C22 | semidirect |
| 22. #97×C37 | C22 | semidirect |
| 23. C4×C8×C37 | C22 | semidirect |
| 86. C4×M16 | D37 | semidirect |
| 87. C37 | #2921 | semidirect |
| 101. #97 | C2×D37 | semidirect |
| 103. 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×#11924493 | 2 |
| #14557595 | 2 |
| #14557592 | 2 |
| #14557556 | 2 |
| #14557496 | 2 |
| C4×#10596934 | 2 |
| C4×M16×C37 | 2 |
| #2921 | 37 |