Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
426 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 426 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. #14271834 | C2 | semidirect |
| 2. D4×Dic58 | C2 | semidirect |
| 3. #14271510 | C2 | semidirect |
| 4. #14271508 | C2 | semidirect |
| 5. #14271443 | C2 | semidirect |
| 6. #14271442 | C2 | semidirect |
| 7. #14271358 | C2 | semidirect |
| 8. #14271356 | C2 | semidirect |
| 9. C8×Dic58 | C2 | semidirect |
| 10. #14271243 | C2 | semidirect |
| 11. C4×D8×C29 | C2 | semidirect |
| 81. D4×C29 | #41 | semidirect |
| 102. Dic58 | D8 | semidirect |
| 136. C4×D8 | D29 | semidirect |
| 172. C29 | #3358 | semidirect |
| 222. D4 | #90805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271834 | 2 |
| D4×Dic58 | 2 |
| #14271510 | 2 |
| #14271508 | 2 |
| #14271443 | 2 |
| #14271442 | 2 |
| #14271358 | 2 |
| #14271356 | 2 |
| C8×Dic58 | 2 |
| #14271243 | 2 |
| C4×D8×C29 | 2 |
| #3358 | 29 |