Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 125 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. Q8×Dic58 | C2 | semidirect |
| 3. #14271510 | C2 | semidirect |
| 4. #14271508 | C2 | semidirect |
| 5. #14271453 | C2 | semidirect |
| 6. #14271452 | C2 | semidirect |
| 7. #14271363 | C2 | semidirect |
| 8. #14271361 | C2 | semidirect |
| 9. C8×Dic58 | C2 | semidirect |
| 10. #14271248 | C2 | semidirect |
| 11. C4×SD16×C29 | C2 | semidirect |
| 77. Q8×C29 | #41 | semidirect |
| 99. Dic58 | SD16 | semidirect |
| 131. C4×SD16 | D29 | semidirect |
| 166. C29 | #3362 | semidirect |
| 206. Q8 | #90805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic58 | 2 |
| #14271834 | 2 |
| #14271510 | 2 |
| #14271508 | 2 |
| #14271453 | 2 |
| #14271452 | 2 |
| #14271363 | 2 |
| #14271361 | 2 |
| C8×Dic58 | 2 |
| #14271248 | 2 |
| C4×SD16×C29 | 2 |
| #3362 | 29 |