Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1512 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 1512 conjugacy classes of subgroups — too many to draw. Only its 549 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×#15690856 | C2 | semidirect |
| 2. #20261540 | C2 | direct (N × H) |
| 3. C2×#15690838 | C2 | semidirect |
| 4. C2×#15690832 | C2 | semidirect |
| 5. C22×D776 | C2 | semidirect |
| 6. C2×#131×C97 | C2 | semidirect |
| 8. #15690856 | C22 | semidirect |
| 10. C2×#13095511 | C22 | semidirect |
| 11. C22×D388 | C22 | semidirect |
| 13. #15690838 | C22 | semidirect |
| 14. #15690832 | C22 | semidirect |
| 15. C2×Dic388 | C22 | semidirect |
| 16. C2×#13095500 | C22 | semidirect |
| 17. C2×D776 | C22 | semidirect |
| 18. C2×D776 | C22 | semidirect |
| 19. C2×D776 | C22 | semidirect |
| 21. #131×C97 | C22 | semidirect |
| 22. C2×M16×C97 | C22 | semidirect |
| 23. C22×C8×C97 | C22 | semidirect |
| 27. #13095511 | C23 | semidirect |
| 32. C2×D388 | C23 | semidirect |
| 36. Dic388 | C23 | semidirect |
| 37. #13095500 | C23 | semidirect |
| 38. D776 | C23 | semidirect |
| 39. D776 | C23 | semidirect |
| 45. M16×C97 | C23 | semidirect |
| 48. C2×C8×C97 | C23 | semidirect |
| 80. C2×C97 | #576 | semidirect |
| 84. C97 | C2×#576 | semidirect |
| 90. C2×#131 | D97 | semidirect |
| 105. #131 | C2×D97 | semidirect |
| 106. C2×M16 | C2×D97 | semidirect |
| 107. C22×C8 | C2×D97 | semidirect |
| 129. M16 | C22×D97 | semidirect |
| 132. C2×C8 | C22×D97 | semidirect |
| 165. C2 | #20261540 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690856 | 2 |
| #20261540 | 2 |
| C2×#15690838 | 2 |
| C2×#15690832 | 2 |
| C22×D776 | 2 |
| C2×#131×C97 | 2 |
| C2×#576 | 97 |