Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
292 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 3. #14272128 | C2 | semidirect |
| 4. C2×#11745208 | C2 | semidirect |
| 5. #14272039 | C2 | semidirect |
| 6. #14272033 | C2 | semidirect |
| 12. #11745346 | C4 | semidirect |
| 19. #11745224 | C4 | semidirect |
| 23. C29×#102 | C4 | semidirect |
| 24. #11745180 | C4 | semidirect |
| 25. #11745164 | C4 | semidirect |
| 26. #11745158 | C4 | semidirect |
| 132. #102 | #1181 | semidirect |
| 136. C29 | #1765 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745346 | 2 |
| C2×#11745224 | 2 |
| #14272128 | 2 |
| C2×#11745208 | 2 |
| #14272039 | 2 |
| #14272033 | 2 |
| #14271156 | 2 |
| #1765 | 29 |