Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
512 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 269 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. #14271199 | C2 | direct (N × H) |
| 4. C2×#11745155 | C2 | semidirect |
| 5. C2×#11745156 | C2 | semidirect |
| 18. C22×#6597 | C4 | semidirect |
| 22. #11745156 | C22 | semidirect |
| 23. #11745155 | C22 | semidirect |
| 43. C2×#6597 | C2×C4 | semidirect |
| 85. C2×C29 | #427 | semidirect |
| 105. C29 | C2×#427 | semidirect |
| 160. C2 | #14271199 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#6597 | 2 |
| C2×#11745288 | 2 |
| #14271199 | 2 |
| C2×#11745155 | 2 |
| C2×#11745156 | 2 |
| C2×C29×#117 | 2 |
| C2×#427 | 29 |