Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
362 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 362 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. #14558243 | C2 | semidirect |
| 2. #14557887 | C2 | semidirect |
| 3. #14557879 | C2 | semidirect |
| 4. #14557833 | C2 | semidirect |
| 5. #14557828 | C2 | semidirect |
| 6. #14557745 | C2 | semidirect |
| 8. Q8×#64436 | C2 | semidirect |
| 9. C4×#10596941 | C2 | semidirect |
| 10. C4×#10596939 | C2 | semidirect |
| 11. C37×#559 | C2 | semidirect |
| 123. #559 | D37 | semidirect |
| 134. C37 | #3361 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558243 | 2 |
| #14557887 | 2 |
| #14557879 | 2 |
| #14557833 | 2 |
| #14557828 | 2 |
| #14557745 | 2 |
| #14557725 | 2 |
| Q8×#64436 | 2 |
| C4×#10596941 | 2 |
| C4×#10596939 | 2 |
| C37×#559 | 2 |
| #3361 | 37 |