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. #14558243 | C2 | semidirect |
| 2. #14557887 | C2 | semidirect |
| 3. #14557883 | C2 | semidirect |
| 4. #14557840 | C2 | semidirect |
| 5. #14557823 | C2 | semidirect |
| 7. #14557735 | C2 | semidirect |
| 8. Q8×#64436 | C2 | semidirect |
| 9. C4×#10596941 | C2 | semidirect |
| 11. C37×#556 | C2 | semidirect |
| 121. #556 | 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 |
|---|---|
| #14558243 | 2 |
| #14557887 | 2 |
| #14557883 | 2 |
| #14557840 | 2 |
| #14557823 | 2 |
| #14557745 | 2 |
| #14557735 | 2 |
| Q8×#64436 | 2 |
| C4×#10596941 | 2 |
| C4×#10596939 | 2 |
| C37×#556 | 2 |
| #3360 | 37 |