Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
392 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 392 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 |
|---|---|---|
| 1. Q8×Dic58 | C2 | semidirect |
| 2. #14271509 | C2 | semidirect |
| 3. #14271453 | C2 | semidirect |
| 4. #14271360 | C2 | semidirect |
| 5. Q8×#6597 | C2 | semidirect |
| 6. C4×#90783 | C2 | semidirect |
| 44. Q8×C29 | SD16 | semidirect |
| 58. Dic58 | #41 | semidirect |
| 100. C29 | #3362 | semidirect |
| 124. Q8 | #90783 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic58 | 2 |
| #14271509 | 2 |
| #14271453 | 2 |
| #14271360 | 2 |
| Q8×#6597 | 2 |
| C4×#90783 | 2 |
| C29×#550 | 2 |
| #3362 | 29 |