Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
162 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 50 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. Q16×#3866 | C2 | semidirect |
| 3. #14558460 | C2 | semidirect |
| 4. #14558446 | C2 | semidirect |
| 6. C16×#3866 | C2 | semidirect |
| 18. #11924481 | C4 | semidirect |
| 19. #11924480 | C4 | semidirect |
| 20. #11924479 | C4 | semidirect |
| 22. SD32×C37 | C4 | semidirect |
| 33. Q16×C37 | C2×C4 | semidirect |
| 37. Dic148 | C2×C4 | semidirect |
| 41. C16×C37 | C2×C4 | semidirect |
| 42. #10596925 | C2×C4 | semidirect |
| 68. #3866 | SD32 | direct (N × H) |
| 86. C37 | C4×SD32 | semidirect |
| 94. SD32 | #3866 | direct (N × H) |
| 107. Q16 | C2×#3866 | semidirect |
| 121. C16 | C2×#3866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×#3866 | 2 |
| D8×#3866 | 2 |
| #14558460 | 2 |
| #14558446 | 2 |
| #14558445 | 2 |
| C16×#3866 | 2 |
| SD32×D37 | 2 |
| C4×SD32 | 37 |