Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 400 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. #14271716 | C2 | semidirect |
| 3. #14271521 | C2 | semidirect |
| 4. #14271516 | C2 | semidirect |
| 5. #14271173 | C2 | semidirect |
| 6. #14271171 | C2 | semidirect |
| 8. M16×Dic29 | C2 | semidirect |
| 21. #11745252 | C22 | semidirect |
| 22. #11745250 | C22 | semidirect |
| 27. #11745164 | C22 | semidirect |
| 28. #11745163 | C22 | semidirect |
| 29. C8×Dic29 | C22 | semidirect |
| 30. #11745158 | C22 | semidirect |
| 135. C29 | #3140 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271716 | 2 |
| C2×#11745298 | 2 |
| #14271521 | 2 |
| #14271516 | 2 |
| #14271173 | 2 |
| #14271171 | 2 |
| #14271168 | 2 |
| M16×Dic29 | 2 |
| C29×#418 | 2 |
| #3140 | 29 |