Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
388 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 125 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. #14557884 | C2 | semidirect |
| 4. #14557870 | C2 | semidirect |
| 5. #14557828 | C2 | semidirect |
| 6. #14557773 | C2 | semidirect |
| 7. #14557743 | C2 | semidirect |
| 8. #14557687 | C2 | semidirect |
| 10. #103×D37 | C2 | semidirect |
| 11. C4×Q16×C37 | C2 | semidirect |
| 91. D148 | Q16 | semidirect |
| 131. C4×Q16 | D37 | semidirect |
| 134. C37 | #3299 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558243 | 2 |
| Q8×D148 | 2 |
| #14557884 | 2 |
| #14557870 | 2 |
| #14557828 | 2 |
| #14557773 | 2 |
| #14557743 | 2 |
| #14557687 | 2 |
| C8×D148 | 2 |
| #103×D37 | 2 |
| C4×Q16×C37 | 2 |
| #3299 | 37 |