Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
462 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 137 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. #14271487 | C2 | semidirect |
| 3. #14271481 | C2 | semidirect |
| 4. #14271476 | C2 | semidirect |
| 5. #14271206 | C2 | semidirect |
| 6. #14271167 | C2 | semidirect |
| 7. #14271127 | C2 | semidirect |
| 8. C2×C29×#117 | C2 | semidirect |
| 15. C29×#117 | C22 | semidirect |
| 16. C2×C4⋊C4×C29 | C22 | semidirect |
| 17. C2×C4⋊C4×C29 | C22 | semidirect |
| 27. C22⋊#6597 | C22 | semidirect |
| 28. C22⋊#6597 | C22 | semidirect |
| 29. #11745157 | C22 | semidirect |
| 30. #11745157 | C22 | semidirect |
| 31. #11745156 | C22 | semidirect |
| 32. #11745155 | C22 | semidirect |
| 120. C2×#117 | D29 | semidirect |
| 145. #117 | C2×D29 | semidirect |
| 147. C2×C4⋊C4 | C2×D29 | semidirect |
| 148. C2×C4⋊C4 | C2×D29 | semidirect |
| 158. C29 | #3094 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745292 | 2 |
| #14271487 | 2 |
| #14271481 | 2 |
| #14271476 | 2 |
| #14271206 | 2 |
| #14271167 | 2 |
| #14271127 | 2 |
| C2×C29×#117 | 2 |
| #3094 | 29 |