Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1144 conjugacy classes of subgroups; only the 349 normal subgroups are shown.
This group has 1144 conjugacy classes of subgroups — too many to draw. Only its 349 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. #14271024 | C2 | direct (N × H) |
| 4. C2×#11745179 | C2 | semidirect |
| 10. C23×Dic29 | C4 | semidirect |
| 18. #11745179 | C22 | semidirect |
| 36. C22×Dic29 | C2×C4 | semidirect |
| 88. C2×C29 | #381 | semidirect |
| 106. C29 | C2×#381 | semidirect |
| 170. C2 | #14271024 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×Dic29 | 2 |
| C22×C22⋊Dic29 | 2 |
| #14271024 | 2 |
| C2×#11745179 | 2 |
| C22×C22⋊C4×C29 | 2 |
| C2×#381 | 29 |