Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
396 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 396 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. #20261455 | C2 | semidirect |
| 2. #20261081 | C2 | semidirect |
| 3. #20261056 | C2 | semidirect |
| 4. #20261020 | C2 | semidirect |
| 5. #20260962 | C2 | semidirect |
| 6. #20260932 | C2 | semidirect |
| 7. #20260897 | C2 | semidirect |
| 8. C4×#13095501 | C2 | semidirect |
| 9. D4×#11715895 | C2 | semidirect |
| 10. #20260731 | C2 | semidirect |
| 128. C97 | #3304 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261455 | 2 |
| #20261081 | 2 |
| #20261056 | 2 |
| #20261020 | 2 |
| #20260962 | 2 |
| #20260932 | 2 |
| #20260897 | 2 |
| C4×#13095501 | 2 |
| D4×#11715895 | 2 |
| #20260731 | 2 |
| #550×C97 | 2 |
| #3304 | 97 |