Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
616 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 173 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. C22×#10596939 | C2 | semidirect |
| 2. C23×#64436 | C2 | semidirect |
| 3. C2×#11924510 | C2 | semidirect |
| 4. #14557767 | C2 | direct (N × H) |
| 5. C2×#11924469 | C2 | semidirect |
| 6. C2×#11924457 | C2 | semidirect |
| 7. C2×#11924456 | C2 | semidirect |
| 8. C2×#121×C37 | C2 | semidirect |
| 12. C2×#10596939 | C22 | semidirect |
| 16. C22×#64436 | C22 | semidirect |
| 18. #11924510 | C22 | semidirect |
| 21. #11924469 | C22 | semidirect |
| 22. #11924457 | C22 | semidirect |
| 23. #11924456 | C22 | semidirect |
| 28. #121×C37 | C22 | semidirect |
| 63. C2×#64436 | D4 | semidirect |
| 72. C23×C37 | D8 | semidirect |
| 101. #64436 | C2×D4 | semidirect |
| 111. C22×C37 | C2×D8 | semidirect |
| 127. C2×C37 | #466 | semidirect |
| 135. C2×#121 | D37 | semidirect |
| 140. C37 | C2×#466 | semidirect |
| 155. #121 | C2×D37 | semidirect |
| 208. C23 | #10596939 | semidirect |
| 247. C22 | C2×#10596939 | semidirect |
| 259. C2 | #14557767 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10596939 | 2 |
| C23×#64436 | 2 |
| C2×#11924510 | 2 |
| #14557767 | 2 |
| C2×#11924469 | 2 |
| C2×#11924457 | 2 |
| C2×#11924456 | 2 |
| C2×#121×C37 | 2 |
| C2×#466 | 37 |