Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
668 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 165 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×#10596939 | C2 | semidirect |
| 4. C2×#11924532 | C2 | semidirect |
| 5. C2×#11924523 | C2 | semidirect |
| 6. #14557921 | C2 | direct (N × H) |
| 7. C2×#11924446 | C2 | semidirect |
| 8. C22×D8×C37 | C2 | semidirect |
| 13. C2×#10596930 | C22 | semidirect |
| 15. C2×#10596940 | C22 | semidirect |
| 17. C2×#10596939 | C22 | semidirect |
| 20. #11924532 | C22 | semidirect |
| 22. #11924523 | C22 | semidirect |
| 25. #11924446 | C22 | semidirect |
| 29. C2×D8×C37 | C22 | semidirect |
| 56. C2×C8×C37 | D4 | semidirect |
| 63. C2×#64436 | D4 | semidirect |
| 97. C8×C37 | C2×D4 | semidirect |
| 98. #64436 | C2×D4 | semidirect |
| 119. C2×C37 | #496 | semidirect |
| 126. C22×D8 | D37 | semidirect |
| 131. C37 | C2×#496 | semidirect |
| 144. C2×D8 | C2×D37 | semidirect |
| 184. C2×C8 | C22⋊D37 | semidirect |
| 221. C8 | C2×C22⋊D37 | semidirect |
| 242. C2 | #14557921 | 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×#10596939 | 2 |
| C2×#11924532 | 2 |
| C2×#11924523 | 2 |
| #14557921 | 2 |
| C2×#11924446 | 2 |
| C22×D8×C37 | 2 |
| C2×#496 | 37 |