Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
430 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20261285 | C2 | semidirect |
| 2. C4×#13095511 | C2 | semidirect |
| 3. #20261060 | C2 | semidirect |
| 4. #20261021 | C2 | semidirect |
| 5. #20261016 | C2 | semidirect |
| 6. #20260936 | C2 | semidirect |
| 7. #20260931 | C2 | semidirect |
| 8. #20260882 | C2 | semidirect |
| 9. #20260848 | C2 | semidirect |
| 10. #20260837 | C2 | semidirect |
| 11. #432×C97 | C2 | semidirect |
| 107. D388 | #41 | semidirect |
| 114. Dic194 | #41 | semidirect |
| 145. C97 | #3115 | semidirect |
| 156. #432 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261285 | 2 |
| C4×#13095511 | 2 |
| #20261060 | 2 |
| #20261021 | 2 |
| #20261016 | 2 |
| #20260936 | 2 |
| #20260931 | 2 |
| #20260882 | 2 |
| #20260848 | 2 |
| #20260837 | 2 |
| #432×C97 | 2 |
| #3115 | 97 |