Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
584 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 584 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 |
|---|---|---|
| 1. C22×#10596930 | C2 | semidirect |
| 2. C22×#10596940 | C2 | semidirect |
| 4. C2×#11924501 | C2 | semidirect |
| 5. #14557732 | C2 | direct (N × H) |
| 6. C2×#11924465 | C2 | semidirect |
| 7. C2×#11924456 | C2 | semidirect |
| 8. C2×#102×C37 | C2 | semidirect |
| 14. C2×#10596930 | C22 | semidirect |
| 16. C2×#10596940 | C22 | semidirect |
| 21. #11924501 | C22 | semidirect |
| 25. #11924465 | C22 | semidirect |
| 26. #11924456 | C22 | semidirect |
| 30. #102×C37 | C22 | semidirect |
| 52. C2×Dic74 | D4 | semidirect |
| 89. C2×Dic37 | SD16 | semidirect |
| 97. Dic74 | C2×D4 | semidirect |
| 118. Dic37 | C2×SD16 | semidirect |
| 121. C2×C37 | #460 | semidirect |
| 133. C2×#102 | D37 | semidirect |
| 134. C37 | C2×#460 | semidirect |
| 156. #102 | C2×D37 | semidirect |
| 247. C2 | #14557732 | 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 |
| C2×#11924532 | 2 |
| C2×#11924501 | 2 |
| #14557732 | 2 |
| C2×#11924465 | 2 |
| C2×#11924456 | 2 |
| C2×#102×C37 | 2 |
| C2×#460 | 37 |