Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
608 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 197 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 |
|---|---|---|
| 2. C2×#11924498 | C2 | semidirect |
| 3. #14557644 | C2 | direct (N × H) |
| 4. C2×#11924456 | C2 | semidirect |
| 5. C2×#11924446 | C2 | semidirect |
| 6. C2×#106×C37 | C2 | semidirect |
| 9. C2×D296 | C4 | semidirect |
| 13. #11924498 | C22 | semidirect |
| 16. #11924456 | C22 | semidirect |
| 17. #11924446 | C22 | semidirect |
| 20. #106×C37 | C22 | semidirect |
| 27. C2×D148 | C2×C4 | semidirect |
| 31. C2×C8×C37 | C2×C4 | semidirect |
| 40. D296 | C2×C4 | semidirect |
| 56. D148 | C22×C4 | semidirect |
| 58. C8×C37 | C22×C4 | semidirect |
| 73. C2×C37 | #442 | semidirect |
| 80. C2×#106 | D37 | semidirect |
| 83. C37 | C2×#442 | semidirect |
| 95. #106 | C2×D37 | semidirect |
| 111. C2×C8 | C4×D37 | semidirect |
| 136. C8 | C2×C4×D37 | semidirect |
| 150. C2 | #14557644 | 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 |
| C2×#11924498 | 2 |
| #14557644 | 2 |
| C2×#11924456 | 2 |
| C2×#11924446 | 2 |
| C2×#106×C37 | 2 |
| C2×#442 | 37 |