Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
386 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 119 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. #14271718 | C2 | semidirect |
| 3. #14271503 | C2 | semidirect |
| 4. #14271459 | C2 | semidirect |
| 5. #14271453 | C2 | semidirect |
| 6. #14271370 | C2 | semidirect |
| 8. #14271267 | C2 | semidirect |
| 9. #14271264 | C2 | semidirect |
| 10. #14271219 | C2 | semidirect |
| 11. C29×#461 | C2 | semidirect |
| 138. #461 | D29 | semidirect |
| 179. C29 | #3116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271718 | 2 |
| C4×#90807 | 2 |
| #14271503 | 2 |
| #14271459 | 2 |
| #14271453 | 2 |
| #14271370 | 2 |
| #14271322 | 2 |
| #14271267 | 2 |
| #14271264 | 2 |
| #14271219 | 2 |
| C29×#461 | 2 |
| #3116 | 29 |