Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
408 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 117 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. #20261451 | C2 | semidirect |
| 2. #20261407 | C2 | semidirect |
| 3. #20261083 | C2 | semidirect |
| 4. #20261062 | C2 | semidirect |
| 5. #20260972 | C2 | semidirect |
| 6. #20260931 | C2 | semidirect |
| 7. #20260883 | C2 | semidirect |
| 8. C4×#13095498 | C2 | semidirect |
| 9. #20260800 | C2 | semidirect |
| 10. #20260730 | C2 | semidirect |
| 11. #477×C97 | C2 | semidirect |
| 133. C97 | #3305 | semidirect |
| 138. #477 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261451 | 2 |
| #20261407 | 2 |
| #20261083 | 2 |
| #20261062 | 2 |
| #20260972 | 2 |
| #20260931 | 2 |
| #20260883 | 2 |
| C4×#13095498 | 2 |
| #20260800 | 2 |
| #20260730 | 2 |
| #477×C97 | 2 |
| #3305 | 97 |