Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
392 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 123 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. #14271893 | C2 | semidirect |
| 3. #14271508 | C2 | semidirect |
| 4. #14271451 | C2 | semidirect |
| 5. #14271450 | C2 | semidirect |
| 6. #14271362 | C2 | semidirect |
| 7. #14271360 | C2 | semidirect |
| 8. C8×Dic58 | C2 | semidirect |
| 9. #14271254 | C2 | semidirect |
| 10. C4×#90773 | C2 | semidirect |
| 11. C29×#486 | C2 | semidirect |
| 98. Dic58 | SD16 | semidirect |
| 99. Dic58 | #41 | semidirect |
| 124. #486 | D29 | semidirect |
| 166. C29 | #3362 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271893 | 2 |
| #14271833 | 2 |
| #14271508 | 2 |
| #14271451 | 2 |
| #14271450 | 2 |
| #14271362 | 2 |
| #14271360 | 2 |
| C8×Dic58 | 2 |
| #14271254 | 2 |
| C4×#90773 | 2 |
| C29×#486 | 2 |
| #3362 | 29 |