Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
292 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 83 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×#11745170 | C2 | semidirect |
| 3. C2×#11745185 | C2 | semidirect |
| 4. C2×#11745173 | C2 | semidirect |
| 5. #14271129 | C2 | semidirect |
| 6. C2×#11745163 | C2 | semidirect |
| 7. C29×#408 | C2 | semidirect |
| 14. C2×#90785 | C4 | semidirect |
| 15. C2×#90784 | C4 | semidirect |
| 16. C2×#90783 | C4 | semidirect |
| 17. C2×#90782 | C4 | semidirect |
| 119. #408 | D29 | semidirect |
| 146. C29 | #1975 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745312 | 2 |
| C2×#11745170 | 2 |
| C2×#11745185 | 2 |
| C2×#11745173 | 2 |
| #14271129 | 2 |
| C2×#11745163 | 2 |
| C29×#408 | 2 |
| #1975 | 29 |