Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
412 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 125 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. #125×D29 | C2 | semidirect |
| 3. #14271520 | C2 | semidirect |
| 4. #14271519 | C2 | semidirect |
| 5. #14271518 | C2 | semidirect |
| 6. #14271517 | C2 | semidirect |
| 7. #14271516 | C2 | semidirect |
| 8. #103×D29 | C2 | semidirect |
| 10. C4×C8×D29 | C2 | semidirect |
| 11. C29×#488 | C2 | semidirect |
| 14. C29×#125 | C22 | semidirect |
| 21. #11745252 | C22 | semidirect |
| 27. #11745232 | C22 | semidirect |
| 28. C29×#103 | C22 | semidirect |
| 30. C4×C8×C29 | C22 | semidirect |
| 31. #11745183 | C22 | semidirect |
| 34. #11745164 | C22 | semidirect |
| 35. C8×Dic29 | C22 | semidirect |
| 36. #11745158 | C22 | semidirect |
| 38. C4×#6597 | C22 | semidirect |
| 118. #488 | D29 | direct (N × H) |
| 126. D29 | #488 | direct (N × H) |
| 133. #125 | C2×D29 | semidirect |
| 146. #103 | C2×D29 | semidirect |
| 153. C4×C8 | C2×D29 | semidirect |
| 154. C29 | C2×#488 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #125×D29 | 2 |
| #124×D29 | 2 |
| #14271520 | 2 |
| #14271519 | 2 |
| #14271518 | 2 |
| #14271517 | 2 |
| #14271516 | 2 |
| #103×D29 | 2 |
| #102×D29 | 2 |
| C4×C8×D29 | 2 |
| C29×#488 | 2 |
| C2×#488 | 29 |