Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
340 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 2. #14271572 | C2 | semidirect |
| 3. #14271568 | C2 | semidirect |
| 4. #14271565 | C2 | semidirect |
| 31. M16×C29 | Q8 | semidirect |
| 32. C2×C8×C29 | Q8 | semidirect |
| 108. C29 | #3164 | semidirect |
| 112. M16 | Dic58 | semidirect |
| 113. C2×C8 | Dic58 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271791 | 2 |
| #14271572 | 2 |
| #14271568 | 2 |
| #14271565 | 2 |
| #14271205 | 2 |
| #14271201 | 2 |
| C2×#11745166 | 2 |
| C29×#405 | 2 |
| #3164 | 29 |