Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
206 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 50. Q8×C29 | Q16 | semidirect |
| 63. Dic58 | Q16 | semidirect |
| 107. C29 | #1633 | semidirect |
| 137. Q8 | #90785 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic58 | 2 |
| #14271542 | 2 |
| #14271455 | 2 |
| #14270911 | 2 |
| Q8⋊#6597 | 2 |
| #14270893 | 2 |
| C29×#477 | 2 |
| #1633 | 29 |