Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
394 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 1. #14271775 | C2 | semidirect |
| 3. #14271505 | C2 | semidirect |
| 4. #14271464 | C2 | semidirect |
| 5. #14271369 | C2 | semidirect |
| 7. #14271265 | C2 | semidirect |
| 8. C4×#90773 | C2 | semidirect |
| 9. C29×#433 | C2 | semidirect |
| 22. #11745232 | C22 | semidirect |
| 23. #11745231 | C22 | semidirect |
| 24. C4×Dic58 | C22 | semidirect |
| 25. C29×C4⋊C8 | C22 | semidirect |
| 27. C29×#97 | C22 | semidirect |
| 28. C4×C8×C29 | C22 | semidirect |
| 31. #11745166 | C22 | semidirect |
| 32. #11745165 | C22 | semidirect |
| 33. #11745164 | C22 | semidirect |
| 34. #11745164 | C22 | semidirect |
| 107. #433 | D29 | semidirect |
| 129. C4⋊C8 | C2×D29 | semidirect |
| 135. #97 | C2×D29 | semidirect |
| 136. C4×C8 | C2×D29 | semidirect |
| 137. C29 | #3123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271775 | 2 |
| #14271637 | 2 |
| #14271505 | 2 |
| #14271464 | 2 |
| #14271369 | 2 |
| #14271316 | 2 |
| #14271265 | 2 |
| C4×#90773 | 2 |
| C29×#433 | 2 |
| #3123 | 29 |