Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
368 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 191 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. #20261856 | C2 | direct (N × H) |
| 2. C2×#15690907 | C2 | semidirect |
| 3. C2×#15690906 | C2 | semidirect |
| 4. C2×#15690905 | C2 | semidirect |
| 5. C22×#13095523 | C2 | semidirect |
| 7. #15690907 | C22 | semidirect |
| 8. #15690906 | C22 | semidirect |
| 9. #15690905 | C22 | semidirect |
| 13. C2×#13095523 | C22 | semidirect |
| 66. C2×C97 | #504 | semidirect |
| 70. C97 | C2×#504 | semidirect |
| 137. C2 | #20261856 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261856 | 2 |
| C2×#15690907 | 2 |
| C2×#15690906 | 2 |
| C2×#15690905 | 2 |
| C22×#13095523 | 2 |
| C2×#15690897 | 2 |
| C2×#504 | 97 |