Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
800 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 249 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. #14271638 | C2 | semidirect |
| 3. #14271136 | C2 | semidirect |
| 4. C2×#11745154 | C2 | semidirect |
| 5. C29×#518 | C2 | semidirect |
| 10. C2×#90807 | C4 | semidirect |
| 11. C2×D4×D29 | C4 | semidirect |
| 14. C29×#117 | C22 | semidirect |
| 15. C2×C22⋊C4×C29 | C22 | semidirect |
| 16. C2×C22⋊Dic29 | C22 | semidirect |
| 18. #11745288 | C22 | semidirect |
| 19. #11745154 | C22 | semidirect |
| 21. C23×D29 | C2×C4 | semidirect |
| 29. C2×C22⋊D29 | C2×C4 | semidirect |
| 32. C22×Dic29 | C2×C4 | semidirect |
| 37. C2×D116 | C2×C4 | semidirect |
| 38. C2×C4×D29 | C2×C4 | semidirect |
| 39. C2×Dic58 | C2×C4 | semidirect |
| 90. #518 | D29 | semidirect |
| 109. #117 | C2×D29 | semidirect |
| 111. C2×C22⋊C4 | C2×D29 | semidirect |
| 113. C29 | #2883 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745359 | 2 |
| #14271638 | 2 |
| #14271136 | 2 |
| C2×#11745154 | 2 |
| C29×#518 | 2 |
| #2883 | 29 |