Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
216 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 56 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. #14558548 | C2 | semidirect |
| 4. M16×#3866 | C2 | semidirect |
| 5. #14558416 | C2 | semidirect |
| 6. #14558405 | C2 | semidirect |
| 23. #11924455 | C4 | semidirect |
| 24. #11924452 | C4 | semidirect |
| 25. #11924452 | C4 | semidirect |
| 26. #101×C37 | C4 | semidirect |
| 113. C37 | #1932 | semidirect |
| 128. #101 | #3866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558548 | 2 |
| #14558532 | 2 |
| C2×#11924601 | 2 |
| M16×#3866 | 2 |
| #14558416 | 2 |
| #14558405 | 2 |
| #14557516 | 2 |
| #1932 | 37 |