Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
146 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 46 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. #14558577 | C2 | semidirect |
| 2. #14558575 | C2 | semidirect |
| 3. #14558462 | C2 | semidirect |
| 4. #14558448 | C2 | semidirect |
| 5. #14558447 | C2 | semidirect |
| 6. C16×#3866 | C2 | semidirect |
| 18. #11924482 | C4 | semidirect |
| 19. #11924481 | C4 | semidirect |
| 20. #11924477 | C4 | semidirect |
| 22. SD32×C37 | C4 | semidirect |
| 79. C37 | #2178 | semidirect |
| 86. SD32 | #3866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558577 | 2 |
| #14558575 | 2 |
| #14558462 | 2 |
| #14558448 | 2 |
| #14558447 | 2 |
| C16×#3866 | 2 |
| #14557964 | 2 |
| #2178 | 37 |