Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
360 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 109 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. C42×Dic37 | C2 | semidirect |
| 6. #14557292 | C2 | semidirect |
| 7. C37×#339 | C2 | semidirect |
| 10. #11924501 | C4 | semidirect |
| 11. #11924498 | C4 | semidirect |
| 18. #11924464 | C4 | semidirect |
| 19. #11924462 | C4 | semidirect |
| 39. M16×C37 | C2×C4 | semidirect |
| 45. C42×C37 | C2×C4 | semidirect |
| 52. C4×Dic37 | C2×C4 | semidirect |
| 56. #10596934 | C2×C4 | semidirect |
| 78. D148 | C42 | semidirect |
| 83. Dic74 | C42 | semidirect |
| 101. Dic37 | #104 | semidirect |
| 114. #339 | D37 | semidirect |
| 115. C37 | C4×#104 | semidirect |
| 149. M16 | C4×D37 | semidirect |
| 165. 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 |
| C42×Dic37 | 2 |
| #14557292 | 2 |
| C37×#339 | 2 |
| C4×#104 | 37 |