Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
348 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 129 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. C2×#11924446 | C2 | semidirect |
| 4. C2×C4×#64436 | C2 | semidirect |
| 6. #14557287 | C2 | semidirect |
| 7. C37×#336 | C2 | semidirect |
| 11. C2×#10596929 | C4 | semidirect |
| 16. #11924448 | C4 | semidirect |
| 60. C2×C4×C37 | M16 | semidirect |
| 80. #64436 | C22⋊C4 | semidirect |
| 111. #336 | D37 | semidirect |
| 112. C37 | #1753 | semidirect |
| 175. C2×C4 | #10596929 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10596929 | 2 |
| C2×#11924448 | 2 |
| C2×#11924446 | 2 |
| C2×C4×#64436 | 2 |
| C4×#10596938 | 2 |
| #14557287 | 2 |
| C37×#336 | 2 |
| #1753 | 37 |