Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
794 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 165 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. C2×#11745297 | C2 | semidirect |
| 2. #14271353 | C2 | direct (N × H) |
| 3. C2×#11745182 | C2 | semidirect |
| 10. C23×Dic29 | C22 | semidirect |
| 12. C2×C22⋊Dic29 | C22 | semidirect |
| 14. #11745297 | C22 | semidirect |
| 16. #11745182 | C22 | semidirect |
| 35. C22×Dic29 | C23 | semidirect |
| 38. C22⋊Dic29 | C23 | semidirect |
| 85. C2×C29 | #458 | semidirect |
| 99. C29 | C2×#458 | semidirect |
| 163. C2 | #14271353 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745297 | 2 |
| #14271353 | 2 |
| C2×#11745182 | 2 |
| C2×C29×H(5,𝔽2) | 2 |
| C2×#458 | 29 |