Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
1036 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 1036 conjugacy classes of subgroups — too many to draw. Only its 253 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. C23×Dic74 | C2 | semidirect |
| 4. #14557446 | C2 | direct (N × H) |
| 5. C2×#11924443 | C2 | semidirect |
| 6. C2×#95×C37 | C2 | semidirect |
| 10. C22×Dic74 | C22 | semidirect |
| 17. #11924443 | C22 | semidirect |
| 20. #95×C37 | C22 | semidirect |
| 26. C23×D37 | Q8 | semidirect |
| 62. C22×D37 | C2×Q8 | semidirect |
| 99. C2×C37 | #393 | semidirect |
| 111. C2×#95 | D37 | semidirect |
| 112. C37 | C2×#393 | semidirect |
| 126. #95 | C2×D37 | semidirect |
| 205. C2 | #14557446 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic74 | 2 |
| C22×#10596938 | 2 |
| #14557446 | 2 |
| C2×#11924443 | 2 |
| C2×#95×C37 | 2 |
| C2×#393 | 37 |