Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
300 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 300 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×C8×#1181 | C2 | semidirect |
| 5. #14272039 | C2 | semidirect |
| 6. #14272033 | C2 | semidirect |
| 10. #11745348 | C4 | semidirect |
| 19. #11745226 | C4 | semidirect |
| 23. C29×#103 | C4 | semidirect |
| 24. #11745183 | C4 | semidirect |
| 25. #11745169 | C4 | semidirect |
| 26. #11745157 | C4 | semidirect |
| 130. #103 | #1181 | semidirect |
| 136. C29 | #1764 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745348 | 2 |
| C2×#11745226 | 2 |
| #14272128 | 2 |
| C2×C8×#1181 | 2 |
| #14272039 | 2 |
| #14272033 | 2 |
| #14271158 | 2 |
| #1764 | 29 |