Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
376 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 141 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. #14271794 | C2 | semidirect |
| 3. #14271472 | C2 | semidirect |
| 4. #14271461 | C2 | semidirect |
| 5. #14271451 | C2 | semidirect |
| 6. #14271446 | C2 | semidirect |
| 7. #14271205 | C2 | semidirect |
| 8. C2×#11745156 | C2 | semidirect |
| 9. #14271191 | C2 | semidirect |
| 42. #41×C29 | Q8 | semidirect |
| 164. C29 | #3084 | semidirect |
| 166. #41 | Dic58 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271794 | 2 |
| #14271646 | 2 |
| #14271472 | 2 |
| #14271461 | 2 |
| #14271451 | 2 |
| #14271446 | 2 |
| #14271205 | 2 |
| C2×#11745156 | 2 |
| #14271191 | 2 |
| #14271159 | 2 |
| C29×#417 | 2 |
| #3084 | 29 |