Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#15690838 | C2 | semidirect |
| 2. C22×D776 | C2 | semidirect |
| 3. #20261304 | C2 | semidirect |
| 4. #20261209 | C2 | semidirect |
| 5. #20260951 | C2 | semidirect |
| 6. #20260931 | C2 | semidirect |
| 7. #20260741 | C2 | semidirect |
| 8. #20260732 | C2 | semidirect |
| 9. #424×C97 | C2 | semidirect |
| 14. C2×#13095500 | C22 | semidirect |
| 17. C2×D776 | C22 | semidirect |
| 18. #15690807 | C22 | semidirect |
| 19. #15690798 | C22 | semidirect |
| 22. C4×D388 | C22 | semidirect |
| 26. #15690735 | C22 | semidirect |
| 27. #15690732 | C22 | semidirect |
| 28. #15690732 | C22 | semidirect |
| 32. C4⋊C8×C97 | C22 | semidirect |
| 44. C2×D388 | D4 | semidirect |
| 122. C97 | #3041 | semidirect |
| 129. #424 | D97 | semidirect |
| 151. C4⋊C8 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690838 | 2 |
| C22×D776 | 2 |
| #20261304 | 2 |
| #20261209 | 2 |
| #20260951 | 2 |
| #20260931 | 2 |
| #20260741 | 2 |
| #20260732 | 2 |
| #424×C97 | 2 |
| #3041 | 97 |