Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
332 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 93 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. #41×Dic29 | C2 | semidirect |
| 2. #14271180 | C2 | semidirect |
| 3. C2×#11745185 | C2 | semidirect |
| 4. #14271137 | C2 | semidirect |
| 5. #14270935 | C2 | semidirect |
| 6. #14270924 | C2 | semidirect |
| 11. C29×#137 | C4 | semidirect |
| 13. C29×AGL(1,ℤ/8) | C4 | semidirect |
| 37. C2×Q8×C29 | C2×C4 | semidirect |
| 41. C2×D4×C29 | C2×C4 | semidirect |
| 53. M16×C29 | C2×C4 | semidirect |
| 140. #137 | Dic29 | semidirect |
| 142. AGL(1,ℤ/8) | Dic29 | semidirect |
| 158. C29 | #1906 | semidirect |
| 167. C2×Q8 | C2×Dic29 | semidirect |
| 171. C2×D4 | C2×Dic29 | semidirect |
| 185. M16 | C2×Dic29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×Dic29 | 2 |
| #14271180 | 2 |
| C2×#11745185 | 2 |
| #14271137 | 2 |
| #14270935 | 2 |
| #14270924 | 2 |
| C29×#575 | 2 |
| #1906 | 29 |