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. #20261088 | C2 | semidirect |
| 4. #20261033 | C2 | semidirect |
| 5. #20261017 | C2 | semidirect |
| 6. #20260956 | C2 | semidirect |
| 8. C8×Dic194 | C2 | semidirect |
| 9. C4×Dic388 | C2 | semidirect |
| 10. #20260826 | C2 | semidirect |
| 118. C97 | #3365 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261471 | 2 |
| #20261460 | 2 |
| #20261088 | 2 |
| #20261033 | 2 |
| #20261017 | 2 |
| #20260956 | 2 |
| #20260932 | 2 |
| C8×Dic194 | 2 |
| C4×Dic388 | 2 |
| #20260826 | 2 |
| #486×C97 | 2 |
| #3365 | 97 |