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. #14271191 | C2 | direct (N × H) |
| 4. C2×#11745162 | C2 | semidirect |
| 18. #11745162 | C22 | semidirect |
| 72. C2×C29 | #424 | semidirect |
| 88. C29 | C2×#424 | semidirect |
| 136. C2 | #14271191 | 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 |
| #14271191 | 2 |
| C2×#11745162 | 2 |
| C22×M16×C29 | 2 |
| C2×#424 | 29 |