Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
652 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 213 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 |
|---|---|---|
| 2. C2×Q8×Dic37 | C2 | semidirect |
| 5. #14557425 | C2 | semidirect |
| 6. #14557398 | C2 | semidirect |
| 7. #14557380 | C2 | semidirect |
| 8. C42×Dic37 | C2 | semidirect |
| 9. C37×#391 | C2 | semidirect |
| 12. #11924525 | C4 | semidirect |
| 33. C2×Q8×C37 | C2×C4 | semidirect |
| 51. #10596938 | C2×C4 | semidirect |
| 57. C4×Dic37 | C2×C4 | semidirect |
| 105. Dic37 | #124 | semidirect |
| 116. #391 | D37 | semidirect |
| 122. C37 | C4×#124 | semidirect |
| 146. C2×Q8 | C4×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924525 | 2 |
| C2×Q8×Dic37 | 2 |
| C2×#11924498 | 2 |
| #14557435 | 2 |
| #14557425 | 2 |
| #14557398 | 2 |
| #14557380 | 2 |
| C42×Dic37 | 2 |
| C37×#391 | 2 |
| C4×#124 | 37 |