Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
350 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 117 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. #14558253 | C2 | semidirect |
| 2. #14558240 | C2 | semidirect |
| 3. #14557886 | C2 | semidirect |
| 4. #14557884 | C2 | semidirect |
| 5. #14557839 | C2 | semidirect |
| 6. #14557823 | C2 | semidirect |
| 8. #14557738 | C2 | semidirect |
| 9. C8×Dic74 | C2 | semidirect |
| 10. #14557624 | C2 | semidirect |
| 132. C37 | #3360 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558253 | 2 |
| #14558240 | 2 |
| #14557886 | 2 |
| #14557884 | 2 |
| #14557839 | 2 |
| #14557823 | 2 |
| #14557746 | 2 |
| #14557738 | 2 |
| C8×Dic74 | 2 |
| #14557624 | 2 |
| C4×D8×C37 | 2 |
| #3360 | 37 |