Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
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×Dic194 | C2 | semidirect |
| 2. #20261087 | C2 | semidirect |
| 3. #20261065 | C2 | semidirect |
| 4. #20261017 | C2 | semidirect |
| 5. #20260962 | C2 | semidirect |
| 6. #20260940 | C2 | semidirect |
| 7. #20260873 | C2 | semidirect |
| 8. C4×#13095499 | C2 | semidirect |
| 9. D4×#11715895 | C2 | semidirect |
| 10. C2×#15690733 | C2 | semidirect |
| 83. D4×C97 | SD16 | semidirect |
| 102. Dic194 | #41 | semidirect |
| 129. C97 | #3298 | semidirect |
| 217. D4 | #13095499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic194 | 2 |
| #20261087 | 2 |
| #20261065 | 2 |
| #20261017 | 2 |
| #20260962 | 2 |
| #20260940 | 2 |
| #20260873 | 2 |
| C4×#13095499 | 2 |
| D4×#11715895 | 2 |
| C2×#15690733 | 2 |
| #547×C97 | 2 |
| #3298 | 97 |