Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
462 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 139 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. #20261442 | C2 | semidirect |
| 3. #20261082 | C2 | semidirect |
| 4. #20261054 | C2 | semidirect |
| 5. #20261026 | C2 | semidirect |
| 6. #20260964 | C2 | semidirect |
| 7. #20260936 | C2 | semidirect |
| 8. #20260888 | C2 | semidirect |
| 9. C4×#13095500 | C2 | semidirect |
| 10. C2×#15690732 | C2 | semidirect |
| 11. C8×D4×C97 | C2 | semidirect |
| 15. C2×#13095500 | C22 | semidirect |
| 16. #15690810 | C22 | semidirect |
| 19. #15690789 | C22 | semidirect |
| 24. C4×Dic194 | C22 | semidirect |
| 27. C2×C4⋊Dic97 | C22 | semidirect |
| 28. #15690742 | C22 | semidirect |
| 29. #15690742 | C22 | semidirect |
| 30. #15690735 | C22 | semidirect |
| 33. #15690732 | C22 | semidirect |
| 34. #15690732 | C22 | semidirect |
| 35. #15690732 | C22 | semidirect |
| 36. C22×C8×C97 | C22 | semidirect |
| 38. C4⋊C8×C97 | C22 | semidirect |
| 39. C22⋊C8×C97 | C22 | semidirect |
| 40. C4×C8×C97 | C22 | semidirect |
| 83. D4×C97 | SD16 | semidirect |
| 137. C97 | #3295 | semidirect |
| 147. C8×D4 | D97 | semidirect |
| 153. C22×C8 | C2×D97 | semidirect |
| 169. C4⋊C8 | C2×D97 | semidirect |
| 176. C22⋊C8 | C2×D97 | semidirect |
| 177. C4×C8 | C2×D97 | semidirect |
| 231. D4 | #13095500 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261442 | 2 |
| D4×D388 | 2 |
| #20261082 | 2 |
| #20261054 | 2 |
| #20261026 | 2 |
| #20260964 | 2 |
| #20260936 | 2 |
| #20260888 | 2 |
| C4×#13095500 | 2 |
| C2×#15690732 | 2 |
| C8×D4×C97 | 2 |
| #3295 | 97 |