Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
482 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 482 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. C2×#15690829 | C2 | semidirect |
| 2. C22×Dic388 | C2 | semidirect |
| 3. #20261391 | C2 | semidirect |
| 4. #20261118 | C2 | semidirect |
| 5. #20260977 | C2 | semidirect |
| 6. #20260956 | C2 | semidirect |
| 7. #20260898 | C2 | semidirect |
| 8. #20260873 | C2 | semidirect |
| 9. #20260829 | C2 | semidirect |
| 10. C8×C22⋊D97 | C2 | semidirect |
| 11. #466×C97 | C2 | semidirect |
| 55. Dic388 | D4 | semidirect |
| 116. C22×C97 | #135 | semidirect |
| 137. C97 | #3285 | semidirect |
| 143. #466 | D97 | semidirect |
| 256. C22 | #15690829 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690829 | 2 |
| C22×Dic388 | 2 |
| #20261391 | 2 |
| #20261118 | 2 |
| #20260977 | 2 |
| #20260956 | 2 |
| #20260898 | 2 |
| #20260873 | 2 |
| #20260829 | 2 |
| C8×C22⋊D97 | 2 |
| #466×C97 | 2 |
| #3285 | 97 |