Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1024 conjugacy classes of subgroups; only the 469 normal subgroups are shown.
This group has 1024 conjugacy classes of subgroups — too many to draw. Only its 469 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. #20261485 | C2 | direct (N × H) |
| 2. C2×#15690808 | C2 | semidirect |
| 3. C2×#15690803 | C2 | semidirect |
| 4. C2×#15690802 | C2 | semidirect |
| 6. C2×#15690787 | C2 | semidirect |
| 10. #15690808 | C22 | semidirect |
| 11. #15690803 | C22 | semidirect |
| 12. #15690802 | C22 | semidirect |
| 14. #15690787 | C22 | semidirect |
| 82. C2×C97 | #563 | semidirect |
| 86. C97 | C2×#563 | semidirect |
| 168. C2 | #20261485 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261485 | 2 |
| C2×#15690808 | 2 |
| C2×#15690803 | 2 |
| C2×#15690802 | 2 |
| C2×#15690791 | 2 |
| C2×#15690787 | 2 |
| C2×#124×C97 | 2 |
| C2×#563 | 97 |