Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1008 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 309 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×#90777 | C2 | semidirect |
| 2. C2×#11745288 | C2 | semidirect |
| 3. #14271168 | C2 | direct (N × H) |
| 4. C2×#11745180 | C2 | semidirect |
| 10. C22×D4×C29 | C4 | semidirect |
| 16. #11745288 | C22 | semidirect |
| 17. C2×C4⋊Dic29 | C22 | semidirect |
| 20. C2×#90777 | C22 | semidirect |
| 21. C22×#6597 | C22 | semidirect |
| 22. #11745180 | C22 | semidirect |
| 35. C2×D4×C29 | C2×C4 | semidirect |
| 46. C4⋊Dic29 | C23 | semidirect |
| 50. C2×#6597 | C23 | semidirect |
| 100. C2×C29 | #418 | semidirect |
| 107. C22×D4 | Dic29 | semidirect |
| 120. C29 | C2×#418 | semidirect |
| 133. C2×D4 | C2×Dic29 | semidirect |
| 192. C2 | #14271168 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90777 | 2 |
| C2×#11745288 | 2 |
| #14271168 | 2 |
| C2×#11745180 | 2 |
| C23×D4×C29 | 2 |
| C2×#418 | 29 |