Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
420 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 420 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. D4×Dic58 | C2 | semidirect |
| 2. #14271515 | C2 | semidirect |
| 3. #14271493 | C2 | semidirect |
| 4. #14271445 | C2 | semidirect |
| 5. #14271390 | C2 | semidirect |
| 6. #14271368 | C2 | semidirect |
| 7. #14271301 | C2 | semidirect |
| 8. C4×#90783 | C2 | semidirect |
| 9. D4×#6597 | C2 | semidirect |
| 10. C2×#11745158 | C2 | semidirect |
| 83. D4×C29 | SD16 | semidirect |
| 102. Dic58 | #41 | semidirect |
| 169. C29 | #3298 | semidirect |
| 217. D4 | #90783 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic58 | 2 |
| #14271515 | 2 |
| #14271493 | 2 |
| #14271445 | 2 |
| #14271390 | 2 |
| #14271368 | 2 |
| #14271301 | 2 |
| C4×#90783 | 2 |
| D4×#6597 | 2 |
| C2×#11745158 | 2 |
| C29×#547 | 2 |
| #3298 | 29 |