Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
648 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 648 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×D296 | C2 | semidirect |
| 2. C22×#10596939 | C2 | semidirect |
| 3. C2×#11924532 | C2 | semidirect |
| 4. C2×#11924498 | C2 | semidirect |
| 5. #14557727 | C2 | direct (N × H) |
| 6. C2×#11924465 | C2 | semidirect |
| 7. C2×#11924456 | C2 | semidirect |
| 8. C2×#102×C37 | C2 | semidirect |
| 15. C2×D296 | C22 | semidirect |
| 17. C2×#10596939 | C22 | semidirect |
| 20. #11924532 | C22 | semidirect |
| 22. #11924498 | C22 | semidirect |
| 25. #11924465 | C22 | semidirect |
| 26. #11924456 | C22 | semidirect |
| 30. #102×C37 | C22 | semidirect |
| 51. C2×D148 | D4 | semidirect |
| 92. C2×Dic37 | D8 | semidirect |
| 100. D148 | C2×D4 | semidirect |
| 125. Dic37 | C2×D8 | semidirect |
| 128. C2×C37 | #459 | semidirect |
| 141. C2×#102 | D37 | semidirect |
| 142. C37 | C2×#459 | semidirect |
| 164. #102 | C2×D37 | semidirect |
| 263. C2 | #14557727 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D296 | 2 |
| C22×#10596939 | 2 |
| C2×#11924532 | 2 |
| C2×#11924498 | 2 |
| #14557727 | 2 |
| C2×#11924465 | 2 |
| C2×#11924456 | 2 |
| C2×#102×C37 | 2 |
| C2×#459 | 37 |