Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1224 conjugacy classes of subgroups; only the 289 normal subgroups are shown.
This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 289 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. C24×Dic29 | C2 | semidirect |
| 2. C2×D4×Dic29 | C2 | semidirect |
| 3. #14271043 | C2 | semidirect |
| 4. #14271038 | C2 | semidirect |
| 5. #14271019 | C2 | semidirect |
| 6. C22⋊C4×Dic29 | C2 | semidirect |
| 13. C23×Dic29 | C22 | semidirect |
| 14. C29×#120 | C4 | semidirect |
| 18. C2×C22⋊Dic29 | C22 | semidirect |
| 20. C2×C4⋊Dic29 | C22 | semidirect |
| 21. C2×C4×Dic29 | C22 | semidirect |
| 22. #11745179 | C22 | semidirect |
| 25. C24×C29 | C2×C4 | semidirect |
| 30. C2×D4×C29 | C2×C4 | semidirect |
| 37. C22×Dic29 | D4 | semidirect |
| 42. C22⋊C4×C29 | C2×C4 | semidirect |
| 56. C23×C29 | C22×C4 | semidirect |
| 63. C2×C4×C29 | C22×C4 | semidirect |
| 82. C22×C29 | C4×D4 | semidirect |
| 90. Dic29 | #120 | direct (N × H) |
| 109. #120 | Dic29 | direct (N × H) |
| 118. C29 | C4×#120 | semidirect |
| 121. C24 | C2×Dic29 | semidirect |
| 126. C2×D4 | C2×Dic29 | semidirect |
| 142. C22⋊C4 | C2×Dic29 | semidirect |
| 154. C23 | C22×Dic29 | semidirect |
| 168. C2×C4 | C22×Dic29 | semidirect |
| 177. C22 | D4×Dic29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×Dic29 | 2 |
| C2×D4×Dic29 | 2 |
| #14271043 | 2 |
| #14271038 | 2 |
| #14271019 | 2 |
| C22⋊C4×Dic29 | 2 |
| C2×C29×#120 | 2 |
| C4×#120 | 29 |