Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
446 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#11924567 | C2 | semidirect |
| 3. #14558299 | C2 | semidirect |
| 4. #14557805 | C2 | semidirect |
| 5. #14557793 | C2 | semidirect |
| 6. #14557582 | C2 | semidirect |
| 7. #14557517 | C2 | semidirect |
| 8. C2×#11924455 | C2 | semidirect |
| 9. C2×#137×C37 | C2 | semidirect |
| 26. #11924472 | C22 | semidirect |
| 27. #11924455 | C22 | semidirect |
| 28. #11924455 | C22 | semidirect |
| 29. #11924453 | C22 | semidirect |
| 34. C2×Q16×C37 | C22 | semidirect |
| 35. C2×SD16×C37 | C22 | semidirect |
| 145. C2×#137 | D37 | semidirect |
| 152. C37 | #3069 | semidirect |
| 166. C2×Q16 | C2×D37 | semidirect |
| 168. C2×SD16 | C2×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558331 | 2 |
| C2×#11924567 | 2 |
| #14558299 | 2 |
| #14557805 | 2 |
| #14557793 | 2 |
| #14557582 | 2 |
| #14557517 | 2 |
| C2×#11924455 | 2 |
| C2×#137×C37 | 2 |
| #3069 | 37 |