Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
524 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 149 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×D776 | C2 | semidirect |
| 2. #20261299 | C2 | semidirect |
| 3. #20260988 | C2 | semidirect |
| 4. #20260971 | C2 | semidirect |
| 5. #20260773 | C2 | semidirect |
| 6. #20260741 | C2 | semidirect |
| 7. C2×#131×C97 | C2 | semidirect |
| 14. #15690784 | C22 | semidirect |
| 17. #15690744 | C22 | semidirect |
| 18. #15690742 | C22 | semidirect |
| 19. #15690732 | C22 | semidirect |
| 23. C2×M16×C97 | C22 | semidirect |
| 25. C22×C8×C97 | C22 | semidirect |
| 48. C2×C8×C97 | D4 | semidirect |
| 94. C97 | #3058 | semidirect |
| 96. C2×#131 | D97 | semidirect |
| 109. C2×M16 | C2×D97 | semidirect |
| 111. C22×C8 | C2×D97 | semidirect |
| 138. C2×C8 | C22⋊D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D776 | 2 |
| #20261299 | 2 |
| #20260988 | 2 |
| #20260971 | 2 |
| #20260773 | 2 |
| #20260741 | 2 |
| C2×#131×C97 | 2 |
| #3058 | 97 |