Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 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. Q8×Dic74 | C2 | semidirect |
| 3. #14557879 | C2 | semidirect |
| 4. #14557878 | C2 | semidirect |
| 5. #14557824 | C2 | semidirect |
| 6. #14557821 | C2 | semidirect |
| 7. #14557731 | C2 | semidirect |
| 8. #14557657 | C2 | semidirect |
| 9. SD16×Dic37 | C2 | semidirect |
| 10. C4×#10596941 | C2 | semidirect |
| 11. C37×#460 | C2 | semidirect |
| 77. Q8×C37 | #41 | semidirect |
| 99. Dic74 | SD16 | semidirect |
| 133. #460 | D37 | semidirect |
| 137. C37 | #3362 | semidirect |
| 206. Q8 | #10596964 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic74 | 2 |
| #14558203 | 2 |
| #14557879 | 2 |
| #14557878 | 2 |
| #14557824 | 2 |
| #14557821 | 2 |
| #14557731 | 2 |
| #14557657 | 2 |
| SD16×Dic37 | 2 |
| C4×#10596941 | 2 |
| C37×#460 | 2 |
| #3362 | 37 |