Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
544 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 205 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 |
|---|---|---|
| 3. #14557631 | C2 | direct (N × H) |
| 4. C2×#11924469 | C2 | semidirect |
| 5. C2×#11924460 | C2 | semidirect |
| 7. C2×#11924447 | C2 | semidirect |
| 8. C2×C4×Q8×C37 | C2 | semidirect |
| 11. C2×#10596941 | C4 | semidirect |
| 19. #11924469 | C22 | semidirect |
| 20. #11924460 | C22 | semidirect |
| 22. #11924447 | C22 | semidirect |
| 25. C4×Q8×C37 | C22 | semidirect |
| 33. C2×Q8×C37 | C2×C4 | semidirect |
| 53. #10596941 | C2×C4 | semidirect |
| 58. C2×#64436 | C2×C4 | semidirect |
| 68. Q8×C37 | C22×C4 | semidirect |
| 88. #64436 | C22×C4 | semidirect |
| 106. C2×C37 | #440 | semidirect |
| 112. C2×C4×Q8 | D37 | semidirect |
| 119. C37 | C2×#440 | semidirect |
| 128. C4×Q8 | C2×D37 | semidirect |
| 144. C2×Q8 | C4×D37 | semidirect |
| 179. Q8 | C2×C4×D37 | semidirect |
| 217. C2 | #14557631 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10596941 | 2 |
| C2×C4×D148 | 2 |
| #14557631 | 2 |
| C2×#11924469 | 2 |
| C2×#11924460 | 2 |
| C2×#11924456 | 2 |
| C2×#11924447 | 2 |
| C2×C4×Q8×C37 | 2 |
| C2×#440 | 37 |