Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
388 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 388 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 |
|---|---|---|
| 3. #14271514 | C2 | semidirect |
| 4. #14271500 | C2 | semidirect |
| 5. #14271458 | C2 | semidirect |
| 6. #14271403 | C2 | semidirect |
| 7. #14271373 | C2 | semidirect |
| 8. #14271317 | C2 | semidirect |
| 10. #103×D29 | C2 | semidirect |
| 11. C4×Q16×C29 | C2 | semidirect |
| 91. D116 | Q16 | semidirect |
| 127. C4×Q16 | D29 | semidirect |
| 163. C29 | #3299 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271873 | 2 |
| Q8×D116 | 2 |
| #14271514 | 2 |
| #14271500 | 2 |
| #14271458 | 2 |
| #14271403 | 2 |
| #14271373 | 2 |
| #14271317 | 2 |
| C8×D116 | 2 |
| #103×D29 | 2 |
| C4×Q16×C29 | 2 |
| #3299 | 29 |