Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
468 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#11924567 | C2 | semidirect |
| 3. C2×#11924542 | C2 | semidirect |
| 4. #14557793 | C2 | direct (N × H) |
| 5. C2×#11924472 | C2 | semidirect |
| 6. C2×#11924455 | C2 | semidirect |
| 7. C2×#11924453 | C2 | semidirect |
| 8. C22×SD16×C37 | C2 | semidirect |
| 11. #11924567 | C22 | semidirect |
| 19. #11924542 | C22 | semidirect |
| 25. #11924472 | C22 | semidirect |
| 26. #11924455 | C22 | semidirect |
| 27. #11924453 | C22 | semidirect |
| 33. C2×SD16×C37 | C22 | semidirect |
| 136. C2×C37 | #471 | semidirect |
| 141. C22×SD16 | D37 | semidirect |
| 147. C37 | C2×#471 | semidirect |
| 161. C2×SD16 | C2×D37 | semidirect |
| 275. C2 | #14557793 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924567 | 2 |
| C2×#11924562 | 2 |
| C2×#11924542 | 2 |
| #14557793 | 2 |
| C2×#11924472 | 2 |
| C2×#11924455 | 2 |
| C2×#11924453 | 2 |
| C22×SD16×C37 | 2 |
| C2×#471 | 37 |