Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 416 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. C4⋊Q8×D29 | C2 | semidirect |
| 3. #14271458 | C2 | semidirect |
| 4. #14271454 | C2 | semidirect |
| 5. #14271450 | C2 | semidirect |
| 6. #14271446 | C2 | semidirect |
| 7. #14271442 | C2 | semidirect |
| 8. #14271204 | C2 | semidirect |
| 9. #14271185 | C2 | semidirect |
| 11. C29×#477 | C2 | semidirect |
| 46. #90809 | Q8 | semidirect |
| 86. Q8×C29 | C2×Q8 | semidirect |
| 100. D116 | C2×Q8 | semidirect |
| 136. #477 | D29 | semidirect |
| 180. C29 | #3079 | semidirect |
| 226. Q8 | Q8×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D29 | 2 |
| C4×#90809 | 2 |
| #14271458 | 2 |
| #14271454 | 2 |
| #14271450 | 2 |
| #14271446 | 2 |
| #14271442 | 2 |
| #14271204 | 2 |
| #14271185 | 2 |
| #14271163 | 2 |
| C29×#477 | 2 |
| #3079 | 29 |