Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
792 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 218 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. C22×#13095520 | C2 | semidirect |
| 2. C23×#11715897 | C2 | semidirect |
| 3. #20261708 | C2 | direct (N × H) |
| 4. C2×#15690867 | C2 | semidirect |
| 5. C2×C22⋊#11715897 | C2 | semidirect |
| 8. C2×#13095520 | C22 | semidirect |
| 12. C22×#11715897 | C22 | semidirect |
| 13. #15690867 | C22 | semidirect |
| 14. C22⋊#11715897 | C22 | semidirect |
| 117. C2×C97 | #408 | semidirect |
| 122. C97 | C2×#408 | semidirect |
| 240. C2 | #20261708 | 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 |
| #20261708 | 2 |
| C2×#15690867 | 2 |
| C2×C22⋊#11715897 | 2 |
| C22×#13095510 | 2 |
| C2×#408 | 97 |