Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
398 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 398 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 |
|---|---|---|
| 2. #14271646 | C2 | semidirect |
| 3. #14271505 | C2 | semidirect |
| 4. #14271499 | C2 | semidirect |
| 5. #14271488 | C2 | semidirect |
| 6. #14271477 | C2 | semidirect |
| 7. #14271205 | C2 | semidirect |
| 8. C2×#11745166 | C2 | semidirect |
| 9. #14271165 | C2 | semidirect |
| 10. #14271160 | C2 | semidirect |
| 11. C29×#408 | C2 | semidirect |
| 138. #408 | D29 | semidirect |
| 174. C29 | #3098 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271741 | 2 |
| #14271646 | 2 |
| #14271505 | 2 |
| #14271499 | 2 |
| #14271488 | 2 |
| #14271477 | 2 |
| #14271205 | 2 |
| C2×#11745166 | 2 |
| #14271165 | 2 |
| #14271160 | 2 |
| C29×#408 | 2 |
| #3098 | 29 |