Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
1036 conjugacy classes of subgroups; only the 261 normal subgroups are shown.
This group has 1036 conjugacy classes of subgroups — too many to draw. Only its 261 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 |
| 3. #14557445 | C2 | direct (N × H) |
| 4. C2×#11924443 | C2 | semidirect |
| 5. C2×#11924443 | C2 | semidirect |
| 9. C22×Dic74 | C22 | semidirect |
| 14. #11924443 | C22 | semidirect |
| 15. #11924443 | C22 | semidirect |
| 25. C24×C37 | Q8 | semidirect |
| 59. C23×C37 | C2×Q8 | semidirect |
| 100. C2×C37 | #393 | semidirect |
| 112. C37 | C2×#393 | semidirect |
| 131. C24 | Dic74 | semidirect |
| 163. C23 | C2×Dic74 | semidirect |
| 205. C2 | #14557445 | 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×C22⋊Dic37 | 2 |
| #14557445 | 2 |
| C2×#11924443 | 2 |
| C22×C22⋊C4×C37 | 2 |
| C2×#393 | 37 |