Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 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 |
|---|---|---|
| 1. #14558256 | C2 | semidirect |
| 2. #14557895 | C2 | semidirect |
| 3. #14557885 | C2 | semidirect |
| 4. #14557825 | C2 | semidirect |
| 5. #14557810 | C2 | semidirect |
| 7. #14557738 | C2 | semidirect |
| 8. #14557664 | C2 | semidirect |
| 9. #14557633 | C2 | semidirect |
| 11. D4×Q8×C37 | C2 | semidirect |
| 124. D4×Q8 | D37 | semidirect |
| 134. C37 | #3367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558256 | 2 |
| #14557895 | 2 |
| #14557885 | 2 |
| #14557825 | 2 |
| #14557810 | 2 |
| #14557748 | 2 |
| #14557738 | 2 |
| #14557664 | 2 |
| #14557633 | 2 |
| C4×#10596939 | 2 |
| D4×Q8×C37 | 2 |
| #3367 | 37 |