Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 133 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. C4⋊Q8×D37 | C2 | semidirect |
| 3. #14557829 | C2 | semidirect |
| 4. #14557825 | C2 | semidirect |
| 5. #14557823 | C2 | semidirect |
| 6. #14557817 | C2 | semidirect |
| 7. #14557811 | C2 | semidirect |
| 8. #14557572 | C2 | semidirect |
| 9. #14557555 | C2 | semidirect |
| 11. C37×#476 | C2 | semidirect |
| 51. #10596964 | Q8 | semidirect |
| 86. D4×C37 | C2×Q8 | semidirect |
| 110. Dic74 | C2×Q8 | semidirect |
| 143. #476 | D37 | semidirect |
| 149. C37 | #3079 | semidirect |
| 229. D4 | Q8×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D37 | 2 |
| C4×#10596964 | 2 |
| #14557829 | 2 |
| #14557825 | 2 |
| #14557823 | 2 |
| #14557817 | 2 |
| #14557811 | 2 |
| #14557572 | 2 |
| #14557555 | 2 |
| #14557531 | 2 |
| C37×#476 | 2 |
| #3079 | 37 |