Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #20261266 | C2 | semidirect |
| 2. #20261136 | C2 | semidirect |
| 3. #20261118 | C2 | semidirect |
| 4. #20261088 | C2 | semidirect |
| 5. #20260976 | C2 | semidirect |
| 6. #20260962 | C2 | semidirect |
| 7. #20260829 | C2 | semidirect |
| 8. #20260826 | C2 | semidirect |
| 9. D8×Dic97 | C2 | semidirect |
| 10. C2×C8×Dic97 | C2 | semidirect |
| 119. C97 | #3168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261266 | 2 |
| #20261136 | 2 |
| #20261118 | 2 |
| #20261088 | 2 |
| #20260976 | 2 |
| #20260962 | 2 |
| #20260829 | 2 |
| #20260826 | 2 |
| D8×Dic97 | 2 |
| C2×C8×Dic97 | 2 |
| #466×C97 | 2 |
| #3168 | 97 |