Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
592 conjugacy classes of subgroups; only the 298 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 298 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 |
|---|---|---|
| 3. #14558498 | C2 | direct (N × H) |
| 4. C2×#11924591 | C2 | semidirect |
| 5. C2×C4×#64438 | C2 | semidirect |
| 7. C2×#10596953 | C4 | semidirect |
| 9. C2×D37⋊C8 | C4 | semidirect |
| 14. #11924591 | C22 | semidirect |
| 15. C4×#64438 | C22 | semidirect |
| 38. #10596953 | C2×C4 | semidirect |
| 39. D37⋊C8 | C2×C4 | semidirect |
| 81. C2×C37 | #405 | semidirect |
| 92. C37 | C2×#405 | semidirect |
| 167. C2 | #14558498 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10596953 | 2 |
| C22×D37⋊C8 | 2 |
| #14558498 | 2 |
| C2×#11924591 | 2 |
| C2×C4×#64438 | 2 |
| C2×#11924494 | 2 |
| C2×#405 | 37 |