Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 115 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. #14558134 | C2 | semidirect |
| 2. #14557934 | C2 | semidirect |
| 3. #14557908 | C2 | semidirect |
| 4. #14557896 | C2 | semidirect |
| 5. #14557785 | C2 | semidirect |
| 6. #14557770 | C2 | semidirect |
| 7. #14557766 | C2 | semidirect |
| 8. #14557643 | C2 | semidirect |
| 9. C4×D296 | C2 | semidirect |
| 10. #14557487 | C2 | semidirect |
| 11. C4×D8×C37 | C2 | semidirect |
| 133. C4×D8 | D37 | semidirect |
| 135. C37 | #3176 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558134 | 2 |
| #14557934 | 2 |
| #14557908 | 2 |
| #14557896 | 2 |
| #14557785 | 2 |
| #14557770 | 2 |
| #14557766 | 2 |
| #14557643 | 2 |
| C4×D296 | 2 |
| #14557487 | 2 |
| C4×D8×C37 | 2 |
| #3176 | 37 |