Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
164 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 31. #90785 | C8 | semidirect |
| 57. #6597 | Q16 | semidirect |
| 94. C29 | C8×Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#6597 | 2 |
| #14271287 | 2 |
| C4×#90785 | 2 |
| #14270915 | 2 |
| #14270895 | 2 |
| C8×#6597 | 2 |
| C29×Q8⋊C8 | 2 |
| C8×Q16 | 29 |