Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#11924558 | C2 | semidirect |
| 2. #14558204 | C2 | semidirect |
| 3. #14558188 | C2 | semidirect |
| 4. #14557906 | C2 | semidirect |
| 5. #14557762 | C2 | semidirect |
| 6. #14557744 | C2 | semidirect |
| 7. #14557729 | C2 | semidirect |
| 8. #14557697 | C2 | semidirect |
| 9. #14557680 | C2 | semidirect |
| 10. C4×#10596930 | C2 | semidirect |
| 11. C8×D4×C37 | C2 | semidirect |
| 81. #10596930 | D4 | semidirect |
| 127. C4×C37 | #135 | semidirect |
| 151. C8×D4 | D37 | semidirect |
| 152. C37 | #3284 | semidirect |
| 272. C4 | #11924558 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924558 | 2 |
| #14558204 | 2 |
| #14558188 | 2 |
| #14557906 | 2 |
| #14557762 | 2 |
| #14557744 | 2 |
| #14557729 | 2 |
| #14557697 | 2 |
| #14557680 | 2 |
| C4×#10596930 | 2 |
| C8×D4×C37 | 2 |
| #3284 | 37 |