Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
468 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 149 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×#11745288 | C2 | semidirect |
| 3. #14271488 | C2 | direct (N × H) |
| 4. C2×#11745166 | C2 | semidirect |
| 5. C2×#11745165 | C2 | semidirect |
| 6. C2×#11745169 | C2 | semidirect |
| 7. C2×#11745169 | C2 | semidirect |
| 8. C2×C29×C22⋊C8 | C2 | semidirect |
| 19. #11745288 | C22 | semidirect |
| 24. C29×C22⋊C8 | C22 | semidirect |
| 25. #11745169 | C22 | semidirect |
| 26. #11745169 | C22 | semidirect |
| 27. #11745166 | C22 | semidirect |
| 28. #11745165 | C22 | semidirect |
| 116. C2×C22⋊C8 | D29 | semidirect |
| 118. C2×C29 | #482 | semidirect |
| 142. C22⋊C8 | C2×D29 | semidirect |
| 143. C29 | C2×#482 | semidirect |
| 225. C2 | #14271488 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745292 | 2 |
| C2×#11745288 | 2 |
| #14271488 | 2 |
| C2×#11745166 | 2 |
| C2×#11745165 | 2 |
| C2×#11745169 | 2 |
| C2×C29×C22⋊C8 | 2 |
| C2×#482 | 29 |