Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
334 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 3. #14271172 | C2 | semidirect |
| 4. #14271070 | C2 | semidirect |
| 5. #14270931 | C2 | semidirect |
| 6. #14270924 | C2 | semidirect |
| 11. C29×#137 | C4 | semidirect |
| 37. C2×Q8×C29 | C2×C4 | semidirect |
| 50. M16×C29 | C2×C4 | semidirect |
| 135. #137 | Dic29 | semidirect |
| 152. C29 | #1882 | semidirect |
| 162. C2×Q8 | C2×Dic29 | semidirect |
| 177. M16 | C2×Dic29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271646 | 2 |
| C2×#11745185 | 2 |
| #14271172 | 2 |
| #14271070 | 2 |
| #14270931 | 2 |
| #14270924 | 2 |
| C2×C29×#137 | 2 |
| #1882 | 29 |