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. #14271833 | C2 | semidirect |
| 2. D4×Dic58 | C2 | semidirect |
| 3. #14271509 | C2 | semidirect |
| 4. #14271508 | C2 | semidirect |
| 5. #14271444 | C2 | semidirect |
| 6. #14271441 | C2 | semidirect |
| 7. #14271356 | C2 | semidirect |
| 8. #14271287 | C2 | semidirect |
| 9. D8×Dic29 | C2 | semidirect |
| 10. C4×#90782 | C2 | semidirect |
| 11. C29×#459 | C2 | semidirect |
| 83. D4×C29 | #41 | semidirect |
| 102. Dic58 | D8 | semidirect |
| 133. #459 | D29 | semidirect |
| 172. C29 | #3358 | semidirect |
| 222. D4 | #90807 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271833 | 2 |
| D4×Dic58 | 2 |
| #14271509 | 2 |
| #14271508 | 2 |
| #14271444 | 2 |
| #14271441 | 2 |
| #14271356 | 2 |
| #14271287 | 2 |
| D8×Dic29 | 2 |
| C4×#90782 | 2 |
| C29×#459 | 2 |
| #3358 | 29 |