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 |
|---|---|---|
| 2. C2×C4×Dic74 | C2 | semidirect |
| 4. #14557635 | C2 | direct (N × H) |
| 5. C2×#11924470 | C2 | semidirect |
| 6. C2×#11924461 | C2 | semidirect |
| 8. C2×#97×C37 | C2 | semidirect |
| 12. C2×#10596930 | C4 | semidirect |
| 15. C4×Dic74 | C22 | semidirect |
| 23. #11924470 | C22 | semidirect |
| 24. #11924461 | C22 | semidirect |
| 29. #97×C37 | C22 | semidirect |
| 45. C2×Dic74 | C2×C4 | semidirect |
| 48. C2×C8×C37 | C2×C4 | semidirect |
| 60. #10596930 | C2×C4 | semidirect |
| 86. Dic74 | C22×C4 | semidirect |
| 88. C8×C37 | C22×C4 | semidirect |
| 106. C2×C37 | #440 | semidirect |
| 118. C2×#97 | D37 | semidirect |
| 119. C37 | C2×#440 | semidirect |
| 140. #97 | C2×D37 | semidirect |
| 160. C2×C8 | C4×D37 | semidirect |
| 199. C8 | C2×C4×D37 | semidirect |
| 217. C2 | #14557635 | 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 |
| C2×C4×Dic74 | 2 |
| C2×C4×D148 | 2 |
| #14557635 | 2 |
| C2×#11924470 | 2 |
| C2×#11924461 | 2 |
| C2×#11924458 | 2 |
| C2×#97×C37 | 2 |
| C2×#440 | 37 |