Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
380 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 66 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. #14272230 | C2 | semidirect |
| 2. C2×#11745215 | C2 | semidirect |
| 3. D29⋊#99 | C2 | semidirect |
| 4. #14272040 | C2 | semidirect |
| 13. C29×#123 | C4 | semidirect |
| 14. #11745299 | C4 | semidirect |
| 15. #11745291 | C4 | semidirect |
| 20. #11745244 | C4 | semidirect |
| 25. C23×D29 | C2×C4 | semidirect |
| 32. C22×C4×C29 | C2×C4 | semidirect |
| 50. C22⋊#1181 | D4 | semidirect |
| 55. C22⋊C4×C29 | C2×C4 | semidirect |
| 56. C22⋊Dic29 | C2×C4 | semidirect |
| 145. #123 | #1181 | semidirect |
| 160. C29 | #1913 | semidirect |
| 181. C22×C4 | C2×#1181 | semidirect |
| 196. C22⋊C4 | C2×#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272230 | 2 |
| C2×#11745215 | 2 |
| D29⋊#99 | 2 |
| #14272040 | 2 |
| #14271724 | 2 |
| #1913 | 29 |