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. C4×#13095511 | C2 | semidirect |
| 2. #20261056 | C2 | semidirect |
| 3. #20261017 | C2 | semidirect |
| 4. #20261012 | C2 | semidirect |
| 5. #20260932 | C2 | semidirect |
| 6. #20260927 | C2 | semidirect |
| 7. #20260878 | C2 | semidirect |
| 8. #20260845 | C2 | semidirect |
| 9. #20260835 | C2 | semidirect |
| 10. #20260792 | C2 | semidirect |
| 11. #532×C97 | C2 | semidirect |
| 109. D388 | #41 | semidirect |
| 114. Dic194 | #41 | semidirect |
| 145. C97 | #3115 | semidirect |
| 146. #532 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13095511 | 2 |
| #20261056 | 2 |
| #20261017 | 2 |
| #20261012 | 2 |
| #20260932 | 2 |
| #20260927 | 2 |
| #20260878 | 2 |
| #20260845 | 2 |
| #20260835 | 2 |
| #20260792 | 2 |
| #532×C97 | 2 |
| #3115 | 97 |