Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
292 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 88 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. #14272129 | C2 | semidirect |
| 4. #14272122 | C2 | semidirect |
| 5. #14272038 | C2 | semidirect |
| 6. #14272034 | C2 | semidirect |
| 9. #11745348 | C4 | semidirect |
| 11. #11745346 | C4 | semidirect |
| 20. #11745225 | C4 | semidirect |
| 21. #11745223 | C4 | semidirect |
| 25. C29×#104 | C4 | semidirect |
| 26. #11745185 | C4 | semidirect |
| 27. #11745173 | C4 | semidirect |
| 28. #11745153 | C4 | semidirect |
| 143. #104 | #1181 | semidirect |
| 149. C29 | #1765 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D29⋊#131 | 2 |
| #14272153 | 2 |
| #14272129 | 2 |
| #14272122 | 2 |
| #14272038 | 2 |
| #14272034 | 2 |
| #104×D29 | 2 |
| #1765 | 29 |