Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
544 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 157 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×#11924534 | C2 | semidirect |
| 5. #14557737 | C2 | direct (N × H) |
| 6. C2×#11924465 | C2 | semidirect |
| 7. C2×#11924459 | C2 | semidirect |
| 8. C2×#103×C37 | C2 | semidirect |
| 18. #11924534 | C22 | semidirect |
| 25. #11924465 | C22 | semidirect |
| 26. #11924459 | C22 | semidirect |
| 30. #103×C37 | C22 | semidirect |
| 84. C2×Dic37 | SD16 | semidirect |
| 111. Dic37 | C2×SD16 | semidirect |
| 113. C2×C37 | #461 | semidirect |
| 125. C2×#103 | D37 | semidirect |
| 126. C37 | C2×#461 | semidirect |
| 148. #103 | C2×D37 | semidirect |
| 231. C2 | #14557737 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10596930 | 2 |
| C22×#10596941 | 2 |
| C2×#11924534 | 2 |
| C2×#11924498 | 2 |
| #14557737 | 2 |
| C2×#11924465 | 2 |
| C2×#11924459 | 2 |
| C2×#103×C37 | 2 |
| C2×#461 | 37 |