Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
360 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 90 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. M16×#3866 | C2 | semidirect |
| 4. #14558412 | C2 | semidirect |
| 13. #11924596 | C4 | semidirect |
| 18. #11924453 | C4 | semidirect |
| 19. #11924452 | C4 | semidirect |
| 20. #100×C37 | C4 | semidirect |
| 35. #10596957 | C2×C4 | semidirect |
| 41. M16×C37 | C2×C4 | semidirect |
| 42. #10596934 | C2×C4 | semidirect |
| 86. #3866 | #100 | direct (N × H) |
| 102. C37 | C4×#100 | semidirect |
| 115. #100 | #3866 | direct (N × H) |
| 135. M16 | C2×#3866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#3866 | 2 |
| D37⋊#100 | 2 |
| M16×#3866 | 2 |
| #14558412 | 2 |
| #100×D37 | 2 |
| C4×#100 | 37 |