Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
388 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 2. C2×#11745179 | C2 | semidirect |
| 3. #14270898 | C2 | direct (N × H) |
| 4. C2×C29×C22⋊C8 | C2 | semidirect |
| 8. C22×D116 | C4 | semidirect |
| 12. #11745292 | C4 | semidirect |
| 15. C2×C4⋊Dic29 | C4 | semidirect |
| 17. C29×C22⋊C8 | C22 | semidirect |
| 19. #11745179 | C22 | semidirect |
| 40. C2×D116 | C2×C4 | semidirect |
| 46. C4⋊Dic29 | C2×C4 | semidirect |
| 105. C2×C22⋊C8 | D29 | semidirect |
| 111. C2×C29 | #327 | semidirect |
| 128. C22⋊C8 | C2×D29 | semidirect |
| 131. C29 | C2×#327 | semidirect |
| 219. C2 | #14270898 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745292 | 2 |
| C2×#11745179 | 2 |
| #14270898 | 2 |
| C2×C29×C22⋊C8 | 2 |
| C2×#327 | 29 |