Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
396 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 2. #20261083 | C2 | semidirect |
| 3. #20261059 | C2 | semidirect |
| 4. #20261017 | C2 | semidirect |
| 5. #20260966 | C2 | semidirect |
| 6. #20260935 | C2 | semidirect |
| 7. #20260895 | C2 | semidirect |
| 8. C4×#13095501 | C2 | semidirect |
| 9. D4×#11715895 | C2 | semidirect |
| 10. #20260729 | C2 | semidirect |
| 11. #556×C97 | C2 | semidirect |
| 128. C97 | #3304 | semidirect |
| 129. #556 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261406 | 2 |
| #20261083 | 2 |
| #20261059 | 2 |
| #20261017 | 2 |
| #20260966 | 2 |
| #20260935 | 2 |
| #20260895 | 2 |
| C4×#13095501 | 2 |
| D4×#11715895 | 2 |
| #20260729 | 2 |
| #556×C97 | 2 |
| #3304 | 97 |