Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
592 conjugacy classes of subgroups; only the 298 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 298 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 |
|---|---|---|
| 3. #20261699 | C2 | direct (N × H) |
| 4. C2×#15690865 | C2 | semidirect |
| 5. C2×C4×#11715897 | C2 | semidirect |
| 7. C2×#13095520 | C4 | semidirect |
| 9. C22×#11715897 | C4 | semidirect |
| 14. #15690865 | C22 | semidirect |
| 15. C4×#11715897 | C22 | semidirect |
| 23. #13095520 | C2×C4 | semidirect |
| 27. C2×#11715897 | C2×C4 | semidirect |
| 78. C2×C97 | #405 | semidirect |
| 82. C97 | C2×#405 | semidirect |
| 160. C2 | #20261699 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095520 | 2 |
| C23×#11715897 | 2 |
| #20261699 | 2 |
| C2×#15690865 | 2 |
| C2×C4×#11715897 | 2 |
| C2×#15690766 | 2 |
| C2×#405 | 97 |