Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
370 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 139 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. #14271513 | C2 | semidirect |
| 3. #14271448 | C2 | semidirect |
| 5. Q8×#6597 | C2 | semidirect |
| 7. C29×#557 | C2 | semidirect |
| 46. Q8×C29 | SD16 | semidirect |
| 71. #557 | D29 | semidirect |
| 98. C29 | #3359 | semidirect |
| 122. Q8 | #90784 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D116 | 2 |
| #14271513 | 2 |
| #14271448 | 2 |
| #14271365 | 2 |
| Q8×#6597 | 2 |
| C4×#90784 | 2 |
| C29×#557 | 2 |
| #3359 | 29 |