Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
460 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 127 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. C2×Q16×D29 | C2 | semidirect |
| 4. #14271420 | C2 | semidirect |
| 5. #14271419 | C2 | semidirect |
| 6. #14271405 | C2 | semidirect |
| 7. #14271404 | C2 | semidirect |
| 8. #14271401 | C2 | semidirect |
| 9. #14271200 | C2 | semidirect |
| 10. #14271170 | C2 | semidirect |
| 11. C29×#467 | C2 | semidirect |
| 140. #467 | D29 | semidirect |
| 178. C29 | #3059 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D29 | 2 |
| C2×#11745263 | 2 |
| #14271736 | 2 |
| #14271420 | 2 |
| #14271419 | 2 |
| #14271405 | 2 |
| #14271404 | 2 |
| #14271401 | 2 |
| #14271200 | 2 |
| #14271170 | 2 |
| C29×#467 | 2 |
| #3059 | 29 |