Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 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. #14558164 | C2 | semidirect |
| 3. #14557835 | C2 | semidirect |
| 4. #14557831 | C2 | semidirect |
| 5. #14557821 | C2 | semidirect |
| 6. #14557811 | C2 | semidirect |
| 7. #14557573 | C2 | semidirect |
| 8. #14557571 | C2 | semidirect |
| 9. #14557559 | C2 | semidirect |
| 14. #11924535 | C22 | semidirect |
| 16. #11924527 | C22 | semidirect |
| 26. #11924470 | C22 | semidirect |
| 27. #11924470 | C22 | semidirect |
| 28. #11924469 | C22 | semidirect |
| 29. #11924468 | C22 | semidirect |
| 30. #11924468 | C22 | semidirect |
| 31. #11924467 | C22 | semidirect |
| 32. #11924465 | C22 | semidirect |
| 33. #11924465 | C22 | semidirect |
| 44. C2×D4×C37 | Q8 | semidirect |
| 136. C37 | #3081 | semidirect |
| 170. C2×D4 | Dic74 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558164 | 2 |
| #14558008 | 2 |
| #14557835 | 2 |
| #14557831 | 2 |
| #14557821 | 2 |
| #14557811 | 2 |
| #14557573 | 2 |
| #14557571 | 2 |
| #14557559 | 2 |
| #14557538 | 2 |
| C2×#102×C37 | 2 |
| #3081 | 37 |