Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
224 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 89 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×#11745160 | C2 | semidirect |
| 2. #14271201 | C2 | semidirect |
| 3. #14270973 | C2 | semidirect |
| 8. C29×#135 | C4 | semidirect |
| 10. C2×Q16×C29 | C4 | semidirect |
| 12. C2×D8×C29 | C4 | semidirect |
| 16. #11745165 | C22 | semidirect |
| 18. #11745160 | C22 | semidirect |
| 92. #135 | Dic29 | semidirect |
| 94. C2×Q16 | Dic29 | semidirect |
| 96. C2×D8 | Dic29 | semidirect |
| 104. C29 | #2145 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745160 | 2 |
| #14271201 | 2 |
| #14270973 | 2 |
| C2×C29×#135 | 2 |
| #2145 | 29 |