Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 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. C2×#15690832 | C2 | semidirect |
| 3. #20261304 | C2 | semidirect |
| 4. #20261215 | C2 | semidirect |
| 5. #20260958 | C2 | semidirect |
| 6. #20260951 | C2 | semidirect |
| 7. #20260936 | C2 | semidirect |
| 8. #20260931 | C2 | semidirect |
| 9. #20260737 | C2 | semidirect |
| 10. C2×#15690732 | C2 | semidirect |
| 11. #424×C97 | C2 | semidirect |
| 17. C2×Dic388 | C22 | semidirect |
| 19. C2×#13095500 | C22 | semidirect |
| 20. C2×#13095500 | C22 | semidirect |
| 22. C2×D776 | C22 | semidirect |
| 28. C4×Dic194 | C22 | semidirect |
| 29. C4×D388 | C22 | semidirect |
| 34. #15690735 | C22 | semidirect |
| 37. #15690732 | C22 | semidirect |
| 41. C4⋊C8×C97 | C22 | semidirect |
| 42. C4⋊C8×C97 | C22 | semidirect |
| 47. #13095511 | D4 | semidirect |
| 155. C97 | #3045 | semidirect |
| 164. #424 | D97 | semidirect |
| 192. C4⋊C8 | C2×D97 | semidirect |
| 193. 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 |
| C2×#15690832 | 2 |
| #20261304 | 2 |
| #20261215 | 2 |
| #20260958 | 2 |
| #20260951 | 2 |
| #20260936 | 2 |
| #20260931 | 2 |
| #20260737 | 2 |
| C2×#15690732 | 2 |
| #424×C97 | 2 |
| #3045 | 97 |