Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
460 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 149 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. #14557865 | C2 | direct (N × H) |
| 4. C2×#11924467 | C2 | semidirect |
| 5. C2×#11924461 | C2 | semidirect |
| 6. C2×#11924459 | C2 | semidirect |
| 8. C2×#106×C37 | C2 | semidirect |
| 21. #11924467 | C22 | semidirect |
| 22. #11924461 | C22 | semidirect |
| 23. #11924459 | C22 | semidirect |
| 28. #106×C37 | C22 | semidirect |
| 104. C2×C37 | #483 | semidirect |
| 113. C2×#106 | D37 | semidirect |
| 117. C37 | C2×#483 | semidirect |
| 134. #106 | C2×D37 | semidirect |
| 213. C2 | #14557865 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924516 | 2 |
| C2×C4⋊C4×D37 | 2 |
| #14557865 | 2 |
| C2×#11924467 | 2 |
| C2×#11924461 | 2 |
| C2×#11924459 | 2 |
| C2×#11924448 | 2 |
| C2×#106×C37 | 2 |
| C2×#483 | 37 |