Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
360 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 107 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. M16×Dic29 | C2 | semidirect |
| 4. #14270932 | C2 | semidirect |
| 5. C29×#343 | C2 | semidirect |
| 15. #11745171 | C4 | semidirect |
| 31. M16×C29 | C2×C4 | semidirect |
| 38. #90777 | C2×C4 | semidirect |
| 79. Dic29 | #100 | semidirect |
| 84. #343 | D29 | semidirect |
| 103. C29 | C4×#100 | semidirect |
| 119. M16 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745255 | 2 |
| C2×#11745171 | 2 |
| M16×Dic29 | 2 |
| #14270932 | 2 |
| C29×#343 | 2 |
| C4×#100 | 29 |