Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
382 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 75 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. #14271734 | C2 | semidirect |
| 2. C2×#11745298 | C2 | semidirect |
| 3. C2×#11745185 | C2 | semidirect |
| 4. #14271168 | C2 | semidirect |
| 5. C2×#11745172 | C2 | semidirect |
| 6. #14270924 | C2 | semidirect |
| 159. C29 | #2003 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271734 | 2 |
| C2×#11745298 | 2 |
| C2×#11745185 | 2 |
| #14271168 | 2 |
| C2×#11745172 | 2 |
| #14270924 | 2 |
| C2×C29×AGL(1,ℤ/8) | 2 |
| #2003 | 29 |