Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
500 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×Dic148 | C2 | semidirect |
| 4. C2×#11924501 | C2 | semidirect |
| 5. #14557754 | C2 | direct (N × H) |
| 6. C2×#11924465 | C2 | semidirect |
| 7. C2×#11924459 | C2 | semidirect |
| 12. C2×Dic148 | C22 | semidirect |
| 19. #11924501 | C22 | semidirect |
| 25. #11924465 | C22 | semidirect |
| 26. #11924459 | C22 | semidirect |
| 112. C2×C37 | #464 | semidirect |
| 124. C37 | C2×#464 | semidirect |
| 227. C2 | #14557754 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic148 | 2 |
| C22×#10596940 | 2 |
| C2×#11924523 | 2 |
| C2×#11924501 | 2 |
| #14557754 | 2 |
| C2×#11924465 | 2 |
| C2×#11924459 | 2 |
| C2×#102×C37 | 2 |
| C2×#464 | 37 |