Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
408 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 408 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. #20261450 | C2 | semidirect |
| 2. #20261081 | C2 | semidirect |
| 3. #20261056 | C2 | semidirect |
| 4. #20261030 | C2 | semidirect |
| 5. #20260969 | C2 | semidirect |
| 6. #20260927 | C2 | semidirect |
| 7. #20260880 | C2 | semidirect |
| 8. C4×#13095498 | C2 | semidirect |
| 9. D4×#11715895 | C2 | semidirect |
| 10. #20260731 | C2 | semidirect |
| 11. #550×C97 | C2 | semidirect |
| 133. C97 | #3305 | semidirect |
| 135. #550 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261450 | 2 |
| #20261081 | 2 |
| #20261056 | 2 |
| #20261030 | 2 |
| #20260969 | 2 |
| #20260927 | 2 |
| #20260880 | 2 |
| C4×#13095498 | 2 |
| D4×#11715895 | 2 |
| #20260731 | 2 |
| #550×C97 | 2 |
| #3305 | 97 |