Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
462 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20261446 | C2 | semidirect |
| 3. #20261083 | C2 | semidirect |
| 4. #20261055 | C2 | semidirect |
| 5. #20260965 | C2 | semidirect |
| 6. #20260936 | C2 | semidirect |
| 7. #20260887 | C2 | semidirect |
| 8. C4×#13095499 | C2 | semidirect |
| 9. #20260800 | C2 | semidirect |
| 10. #102×D97 | C2 | semidirect |
| 11. #476×C97 | C2 | semidirect |
| 14. C2×#13095500 | C22 | semidirect |
| 16. C2×C8×D97 | C22 | semidirect |
| 19. #15690790 | C22 | semidirect |
| 24. C4×Dic194 | C22 | semidirect |
| 27. C4⋊C4×D97 | C22 | semidirect |
| 28. #15690741 | C22 | semidirect |
| 29. #15690733 | C22 | semidirect |
| 30. #15690732 | C22 | semidirect |
| 32. #15690730 | C22 | semidirect |
| 33. #15690730 | C22 | semidirect |
| 34. #15690722 | C22 | semidirect |
| 35. C4×#11715895 | C22 | semidirect |
| 36. C4⋊Q8×C97 | C22 | semidirect |
| 38. #106×C97 | C22 | semidirect |
| 39. C4⋊C8×C97 | C22 | semidirect |
| 101. D388 | SD16 | semidirect |
| 137. C97 | #3295 | semidirect |
| 142. #476 | D97 | semidirect |
| 154. C4⋊Q8 | C2×D97 | semidirect |
| 168. #106 | C2×D97 | semidirect |
| 169. C4⋊C8 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261446 | 2 |
| D4×D388 | 2 |
| #20261083 | 2 |
| #20261055 | 2 |
| #20260965 | 2 |
| #20260936 | 2 |
| #20260887 | 2 |
| C4×#13095499 | 2 |
| #20260800 | 2 |
| #102×D97 | 2 |
| #476×C97 | 2 |
| #3295 | 97 |