Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
680 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 145 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. #14270930 | C2 | semidirect |
| 4. #14270929 | C2 | semidirect |
| 5. C29×#342 | C2 | semidirect |
| 8. C22×C4×D29 | C4 | semidirect |
| 14. C2×#90781 | C4 | semidirect |
| 18. C22⋊C4×D29 | C4 | semidirect |
| 29. C22×C4×C29 | C2×C4 | semidirect |
| 31. C22×Dic29 | C2×C4 | semidirect |
| 39. C22⋊C4×C29 | C2×C4 | semidirect |
| 42. C22⋊Dic29 | C2×C4 | semidirect |
| 113. #342 | D29 | direct (N × H) |
| 122. D29 | #342 | direct (N × H) |
| 136. C29 | C2×#342 | semidirect |
| 154. C22×C4 | C4×D29 | semidirect |
| 162. C22⋊C4 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊C4×D29 | 2 |
| #14270930 | 2 |
| #14270929 | 2 |
| C29×#342 | 2 |
| C2×#342 | 29 |