Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
416 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 137 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×#11745250 | C2 | semidirect |
| 3. #14271457 | C2 | semidirect |
| 4. #14271452 | C2 | semidirect |
| 5. #14271447 | C2 | semidirect |
| 6. #14271442 | C2 | semidirect |
| 7. #14271206 | C2 | semidirect |
| 8. #14271186 | C2 | semidirect |
| 11. C29×#428 | C2 | semidirect |
| 50. #90805 | Q8 | semidirect |
| 104. D116 | C2×Q8 | semidirect |
| 111. Dic58 | C2×Q8 | semidirect |
| 141. #428 | D29 | semidirect |
| 181. C29 | #3079 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745250 | 2 |
| #14271631 | 2 |
| #14271457 | 2 |
| #14271452 | 2 |
| #14271447 | 2 |
| #14271442 | 2 |
| #14271206 | 2 |
| #14271186 | 2 |
| #14271165 | 2 |
| #14271162 | 2 |
| C29×#428 | 2 |
| #3079 | 29 |