Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
348 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 115 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. #20261460 | C2 | semidirect |
| 3. #20261091 | C2 | semidirect |
| 5. #20261034 | C2 | semidirect |
| 6. #20260960 | C2 | semidirect |
| 8. #20260859 | C2 | semidirect |
| 9. C4×#13095501 | C2 | semidirect |
| 10. #20260822 | C2 | semidirect |
| 11. #475×C97 | C2 | semidirect |
| 118. C97 | #3365 | semidirect |
| 124. #475 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261470 | 2 |
| #20261460 | 2 |
| #20261091 | 2 |
| #20261083 | 2 |
| #20261034 | 2 |
| #20260960 | 2 |
| #20260936 | 2 |
| #20260859 | 2 |
| C4×#13095501 | 2 |
| #20260822 | 2 |
| #475×C97 | 2 |
| #3365 | 97 |