Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
368 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 117 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×#11924559 | C2 | semidirect |
| 2. C2×#11924555 | C2 | semidirect |
| 3. #14557964 | C2 | direct (N × H) |
| 4. C2×#11924482 | C2 | semidirect |
| 5. C2×#11924481 | C2 | semidirect |
| 6. C2×#11924477 | C2 | semidirect |
| 7. C2×C16×D37 | C2 | semidirect |
| 8. C2×SD32×C37 | C2 | semidirect |
| 12. #11924559 | C22 | semidirect |
| 14. #11924555 | C22 | semidirect |
| 20. #11924482 | C22 | semidirect |
| 21. #11924481 | C22 | semidirect |
| 22. #11924477 | C22 | semidirect |
| 24. C16×D37 | C22 | semidirect |
| 27. SD32×C37 | C22 | semidirect |
| 96. C2×C37 | #508 | semidirect |
| 105. C2×SD32 | D37 | semidirect |
| 108. C37 | C2×#508 | semidirect |
| 124. SD32 | C2×D37 | semidirect |
| 197. C2 | #14557964 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924559 | 2 |
| C2×#11924555 | 2 |
| #14557964 | 2 |
| C2×#11924482 | 2 |
| C2×#11924481 | 2 |
| C2×#11924477 | 2 |
| C2×C16×D37 | 2 |
| C2×SD32×C37 | 2 |
| C2×#508 | 37 |