Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
410 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 137 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. #14271505 | C2 | semidirect |
| 4. #14271499 | C2 | semidirect |
| 5. #14271494 | C2 | semidirect |
| 6. #14271205 | C2 | semidirect |
| 7. #14271173 | C2 | semidirect |
| 29. #11745166 | C22 | semidirect |
| 30. #11745165 | C22 | semidirect |
| 31. #11745164 | C22 | semidirect |
| 32. #11745164 | C22 | semidirect |
| 149. C29 | #3095 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745286 | 2 |
| C2×#11745288 | 2 |
| #14271505 | 2 |
| #14271499 | 2 |
| #14271494 | 2 |
| #14271205 | 2 |
| #14271173 | 2 |
| C29×#407 | 2 |
| #3095 | 29 |