Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1460 conjugacy classes of subgroups; only the 754 normal subgroups are shown.
This group has 1460 conjugacy classes of subgroups — too many to draw. Only its 754 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. #20261815 | C2 | direct (N × H) |
| 2. C2×#15690898 | C2 | semidirect |
| 3. C2×D97⋊M16 | C2 | semidirect |
| 5. #15690898 | C22 | semidirect |
| 6. C2×#13095521 | C22 | semidirect |
| 7. D97⋊M16 | C22 | semidirect |
| 9. C2×#13095519 | C22 | semidirect |
| 17. #13095521 | C23 | semidirect |
| 19. #13095519 | C23 | semidirect |
| 62. C2×C97 | #568 | semidirect |
| 66. C97 | C2×#568 | semidirect |
| 129. C2 | #20261815 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261815 | 2 |
| C2×#15690898 | 2 |
| C2×D97⋊M16 | 2 |
| C22×#13095512 | 2 |
| C2×#568 | 97 |