Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
526 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 526 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 |
|---|---|---|
| 1. C2×#11745294 | C2 | semidirect |
| 2. C22×#90782 | C2 | semidirect |
| 3. #14271732 | C2 | semidirect |
| 4. #14271378 | C2 | semidirect |
| 5. #14271358 | C2 | semidirect |
| 6. #14271190 | C2 | semidirect |
| 7. #14271167 | C2 | semidirect |
| 8. #14271157 | C2 | semidirect |
| 9. C29×#518 | C2 | semidirect |
| 14. C4×D4×C29 | C22 | semidirect |
| 18. C2×#90783 | C22 | semidirect |
| 22. C2×#90782 | C22 | semidirect |
| 27. #11745237 | C22 | semidirect |
| 28. #11745236 | C22 | semidirect |
| 29. #11745158 | C22 | semidirect |
| 30. #11745157 | C22 | semidirect |
| 31. #11745157 | C22 | semidirect |
| 32. C4⋊#6597 | C22 | semidirect |
| 37. C2×D4×C29 | D4 | semidirect |
| 119. #518 | D29 | semidirect |
| 146. C4×D4 | C2×D29 | semidirect |
| 154. C29 | #3041 | semidirect |
| 169. C2×D4 | D116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745294 | 2 |
| C22×#90782 | 2 |
| #14271732 | 2 |
| #14271378 | 2 |
| #14271358 | 2 |
| #14271190 | 2 |
| #14271167 | 2 |
| #14271157 | 2 |
| C29×#518 | 2 |
| #3041 | 29 |