Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
656 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 181 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×#10596930 | C2 | semidirect |
| 2. C22×#10596940 | C2 | semidirect |
| 3. C22×#10596941 | C2 | semidirect |
| 4. C2×#11924534 | C2 | semidirect |
| 6. #14557904 | C2 | direct (N × H) |
| 7. C2×C8×Dic37 | C2 | semidirect |
| 8. C22×SD16×C37 | C2 | semidirect |
| 13. C2×#10596930 | C22 | semidirect |
| 15. C2×#10596940 | C22 | semidirect |
| 17. C2×#10596941 | C22 | semidirect |
| 20. #11924534 | C22 | semidirect |
| 25. C8×Dic37 | C22 | semidirect |
| 29. C2×SD16×C37 | C22 | semidirect |
| 56. C2×C8×C37 | D4 | semidirect |
| 63. C2×#64436 | D4 | semidirect |
| 88. C2×Dic37 | SD16 | semidirect |
| 96. C8×C37 | C2×D4 | semidirect |
| 97. #64436 | C2×D4 | semidirect |
| 112. Dic37 | C2×SD16 | semidirect |
| 115. C2×C37 | #492 | semidirect |
| 122. C22×SD16 | D37 | semidirect |
| 127. C37 | C2×#492 | semidirect |
| 140. C2×SD16 | C2×D37 | semidirect |
| 180. C2×C8 | C22⋊D37 | semidirect |
| 216. C8 | C2×C22⋊D37 | semidirect |
| 234. C2 | #14557904 | 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×#10596940 | 2 |
| C22×#10596941 | 2 |
| C2×#11924534 | 2 |
| C2×#11924532 | 2 |
| #14557904 | 2 |
| C2×C8×Dic37 | 2 |
| C22×SD16×C37 | 2 |
| C2×#492 | 37 |