Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
272 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 109 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×#90768 | C2 | semidirect |
| 2. C2×#11745166 | C2 | semidirect |
| 3. #14270964 | C2 | direct (N × H) |
| 8. C2×D8×C29 | C4 | semidirect |
| 13. #11745166 | C22 | semidirect |
| 15. C2×#90768 | C22 | semidirect |
| 25. D8×C29 | C2×C4 | semidirect |
| 68. C2×C29 | #357 | semidirect |
| 75. C2×D8 | Dic29 | semidirect |
| 83. C29 | C2×#357 | semidirect |
| 93. D8 | C2×Dic29 | semidirect |
| 131. C2 | #14270964 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90768 | 2 |
| C2×#11745166 | 2 |
| #14270964 | 2 |
| C22×D8×C29 | 2 |
| C2×#357 | 29 |