Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
490 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 133 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×#11745313 | C2 | semidirect |
| 2. C22×#90773 | C2 | semidirect |
| 4. #14271640 | C2 | semidirect |
| 5. #14271388 | C2 | semidirect |
| 6. #14271362 | C2 | semidirect |
| 7. #14271189 | C2 | semidirect |
| 8. #14271167 | C2 | semidirect |
| 9. C29×#416 | C2 | semidirect |
| 17. C2×#90785 | C22 | semidirect |
| 20. C2×#90783 | C22 | semidirect |
| 26. #11745249 | C22 | semidirect |
| 29. C29×#103 | C22 | semidirect |
| 30. C29×#102 | C22 | semidirect |
| 31. #11745162 | C22 | semidirect |
| 49. C2×Dic58 | D4 | semidirect |
| 120. #416 | D29 | semidirect |
| 146. #103 | C2×D29 | semidirect |
| 148. #102 | C2×D29 | semidirect |
| 149. C29 | #3043 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745313 | 2 |
| C22×#90773 | 2 |
| #14271727 | 2 |
| #14271640 | 2 |
| #14271388 | 2 |
| #14271362 | 2 |
| #14271189 | 2 |
| #14271167 | 2 |
| C29×#416 | 2 |
| #3043 | 29 |