Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
280 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 52 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. D29⋊#100 | C2 | semidirect |
| 2. D29⋊#99 | C2 | semidirect |
| 3. #14272066 | C2 | semidirect |
| 4. #14272063 | C2 | semidirect |
| 6. C22×C22⋊D29 | C4 | semidirect |
| 10. C29×#120 | C4 | semidirect |
| 14. #11745297 | C4 | semidirect |
| 18. C22⋊C4×D29 | C4 | semidirect |
| 23. C24×C29 | C2×C4 | semidirect |
| 36. C22×Dic29 | C2×C4 | semidirect |
| 48. C22⋊C4×C29 | C2×C4 | semidirect |
| 51. C22⋊Dic29 | C2×C4 | semidirect |
| 142. #120 | #1181 | semidirect |
| 149. C29 | #2121 | semidirect |
| 152. C24 | C2×#1181 | semidirect |
| 182. C22⋊C4 | C2×#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D29⋊#100 | 2 |
| D29⋊#99 | 2 |
| #14272066 | 2 |
| #14272063 | 2 |
| #14271723 | 2 |
| #2121 | 29 |