Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
516 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 516 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. #14557417 | C2 | semidirect |
| 4. #14557401 | C2 | semidirect |
| 5. C4×#10596936 | C2 | semidirect |
| 7. C43×C37 | C2 | semidirect |
| 9. #11924530 | C4 | direct (N × H) |
| 32. C42×C37 | C2×C4 | semidirect |
| 36. #10596936 | C2×C4 | semidirect |
| 65. C4×C37 | #126 | semidirect |
| 80. C43 | D37 | semidirect |
| 81. C37 | C4×#126 | semidirect |
| 111. C42 | C4×D37 | semidirect |
| 142. C4 | #11924530 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924530 | 2 |
| #14557424 | 2 |
| #14557417 | 2 |
| #14557401 | 2 |
| C4×#10596936 | 2 |
| C4×#10596938 | 2 |
| C43×C37 | 2 |
| C4×#126 | 37 |