Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
598 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 105 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. C22×C22⋊Dic29 | C2 | semidirect |
| 2. C2×#11745182 | C2 | semidirect |
| 3. #14271019 | C2 | semidirect |
| 4. #14270930 | C2 | semidirect |
| 7. C22×D4×C29 | C4 | semidirect |
| 13. C2×C22⋊C4×C29 | C4 | semidirect |
| 25. C24×C29 | C2×C4 | semidirect |
| 37. C22×C4×C29 | C2×C4 | semidirect |
| 38. C22×C4×C29 | C2×C4 | semidirect |
| 52. C22⋊Dic29 | D4 | semidirect |
| 112. C22×C29 | #99 | semidirect |
| 137. C22×D4 | Dic29 | semidirect |
| 148. C2×C22⋊C4 | Dic29 | semidirect |
| 151. C29 | #1898 | semidirect |
| 156. C24 | C2×Dic29 | semidirect |
| 172. C22×C4 | C2×Dic29 | semidirect |
| 173. C22×C4 | C2×Dic29 | semidirect |
| 242. C22 | #11745182 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊Dic29 | 2 |
| C2×#11745182 | 2 |
| #14271019 | 2 |
| #14270930 | 2 |
| C2×C29×#120 | 2 |
| #1898 | 29 |