Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
252 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 68 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. #14272013 | C2 | semidirect |
| 4. Q8⋊#6599 | C2 | semidirect |
| 53. Q8×C29 | M16 | semidirect |
| 72. Dic58 | M16 | semidirect |
| 117. C29 | #1491 | semidirect |
| 151. Q8 | #90796 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272185 | 2 |
| C4×#90796 | 2 |
| #14272013 | 2 |
| Q8⋊#6599 | 2 |
| C4×Q8×D29 | 2 |
| #1491 | 29 |