Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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×Dic388 | C2 | semidirect |
| 2. C22×#13095501 | C2 | semidirect |
| 4. C2×#15690808 | C2 | semidirect |
| 6. #20261126 | C2 | direct (N × H) |
| 7. C2×#15690720 | C2 | semidirect |
| 12. C2×Dic388 | C22 | semidirect |
| 14. C2×#13095501 | C22 | semidirect |
| 19. #15690808 | C22 | semidirect |
| 25. #15690720 | C22 | semidirect |
| 109. C2×C97 | #497 | semidirect |
| 113. C97 | C2×#497 | semidirect |
| 222. C2 | #20261126 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic388 | 2 |
| C22×#13095501 | 2 |
| C22×#13095499 | 2 |
| C2×#15690808 | 2 |
| C2×#15690797 | 2 |
| #20261126 | 2 |
| C2×#15690720 | 2 |
| C22×SD16×C97 | 2 |
| C2×#497 | 97 |