Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
154 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 59 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. #14271285 | C2 | semidirect |
| 2. #14271275 | C2 | semidirect |
| 3. #14270986 | C2 | semidirect |
| 4. #14270976 | C2 | semidirect |
| 5. #14270973 | C2 | semidirect |
| 6. #14270940 | C2 | semidirect |
| 12. C29×SD32 | C4 | semidirect |
| 13. C29×D16 | C4 | semidirect |
| 24. Q16×C29 | C2×C4 | semidirect |
| 28. D8×C29 | C2×C4 | semidirect |
| 37. C16×C29 | C2×C4 | semidirect |
| 80. SD32 | Dic29 | semidirect |
| 81. D16 | Dic29 | semidirect |
| 89. C29 | AGL(1,ℤ/16) | semidirect |
| 93. Q16 | C2×Dic29 | semidirect |
| 97. D8 | C2×Dic29 | semidirect |
| 107. C16 | C2×Dic29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271285 | 2 |
| #14271275 | 2 |
| #14270986 | 2 |
| #14270976 | 2 |
| #14270973 | 2 |
| #14270940 | 2 |
| C29×#509 | 2 |
| AGL(1,ℤ/16) | 29 |