Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1240 conjugacy classes of subgroups; only the 501 normal subgroups are shown.
This group has 1240 conjugacy classes of subgroups — too many to draw. Only its 501 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. #14271899 | C2 | direct (N × H) |
| 2. C2×#11745298 | C2 | semidirect |
| 3. C2×#11745297 | C2 | semidirect |
| 4. C2×C4×Dic58 | C2 | semidirect |
| 5. C2×D4×Dic29 | C2 | semidirect |
| 15. #11745298 | C22 | semidirect |
| 16. #11745297 | C22 | semidirect |
| 17. D4×Dic29 | C22 | semidirect |
| 21. C4×Dic58 | C22 | semidirect |
| 75. C2×C29 | #559 | semidirect |
| 93. C29 | C2×#559 | semidirect |
| 140. C2 | #14271899 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271899 | 2 |
| C2×#11745298 | 2 |
| C2×#11745297 | 2 |
| C2×C4×Dic58 | 2 |
| C2×D4×Dic29 | 2 |
| C2×C29×#127 | 2 |
| C2×#559 | 29 |