Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
430 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 430 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. #14271714 | C2 | semidirect |
| 2. C4×#90809 | C2 | semidirect |
| 3. #14271489 | C2 | semidirect |
| 4. #14271440 | C2 | semidirect |
| 5. #14271363 | C2 | semidirect |
| 6. #14271359 | C2 | semidirect |
| 7. #14271311 | C2 | semidirect |
| 8. #14271274 | C2 | semidirect |
| 9. #14271266 | C2 | semidirect |
| 10. #14271219 | C2 | semidirect |
| 11. C29×#475 | C2 | semidirect |
| 88. Q8×C29 | #41 | semidirect |
| 106. D116 | #41 | semidirect |
| 142. #475 | D29 | semidirect |
| 187. C29 | #3115 | semidirect |
| 233. Q8 | #90809 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271714 | 2 |
| C4×#90809 | 2 |
| #14271489 | 2 |
| #14271440 | 2 |
| #14271363 | 2 |
| #14271359 | 2 |
| #14271311 | 2 |
| #14271274 | 2 |
| #14271266 | 2 |
| #14271219 | 2 |
| C29×#475 | 2 |
| #3115 | 29 |