Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
350 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 123 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. #14558256 | C2 | semidirect |
| 2. #14558243 | C2 | semidirect |
| 3. #14557888 | C2 | semidirect |
| 4. #14557884 | C2 | semidirect |
| 5. #14557841 | C2 | semidirect |
| 6. #14557824 | C2 | semidirect |
| 8. #14557739 | C2 | semidirect |
| 9. C4×#10596930 | C2 | semidirect |
| 11. C8×Q8×C37 | C2 | semidirect |
| 129. C8×Q8 | D37 | semidirect |
| 132. C37 | #3360 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558256 | 2 |
| #14558243 | 2 |
| #14557888 | 2 |
| #14557884 | 2 |
| #14557841 | 2 |
| #14557824 | 2 |
| #14557749 | 2 |
| #14557739 | 2 |
| C4×#10596930 | 2 |
| C4×D296 | 2 |
| C8×Q8×C37 | 2 |
| #3360 | 37 |