Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
320 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 4. M16×Dic37 | C2 | semidirect |
| 5. #14557379 | C2 | semidirect |
| 6. #14557292 | C2 | semidirect |
| 7. C37×#339 | C2 | semidirect |
| 10. #11924501 | C4 | semidirect |
| 11. #11924498 | C4 | semidirect |
| 17. #11924464 | C4 | semidirect |
| 18. #11924462 | C4 | semidirect |
| 39. M16×C37 | C2×C4 | semidirect |
| 45. C42×C37 | C2×C4 | semidirect |
| 51. C4×Dic37 | C2×C4 | semidirect |
| 55. #10596934 | C2×C4 | semidirect |
| 113. #339 | D37 | semidirect |
| 114. C37 | #1759 | semidirect |
| 148. M16 | C4×D37 | semidirect |
| 163. C42 | C4×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558001 | 2 |
| C2×#11924464 | 2 |
| C2×#11924462 | 2 |
| M16×Dic37 | 2 |
| #14557379 | 2 |
| #14557292 | 2 |
| C37×#339 | 2 |
| #1759 | 37 |