Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
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×#15692301 | C2 | semidirect |
| 2. #20265982 | C2 | direct (N × H) |
| 3. C2×#15692283 | C2 | semidirect |
| 4. C2×#15692277 | C2 | semidirect |
| 5. C22×D808 | C2 | semidirect |
| 6. C2×#131×C101 | C2 | semidirect |
| 8. #15692301 | C22 | semidirect |
| 10. C2×#13108074 | C22 | semidirect |
| 11. C22×D404 | C22 | semidirect |
| 13. #15692283 | C22 | semidirect |
| 14. #15692277 | C22 | semidirect |
| 15. C2×Dic404 | C22 | semidirect |
| 16. C2×#13108063 | C22 | semidirect |
| 17. C2×D808 | C22 | semidirect |
| 18. C2×D808 | C22 | semidirect |
| 19. C2×D808 | C22 | semidirect |
| 21. #131×C101 | C22 | semidirect |
| 22. C2×M16×C101 | C22 | semidirect |
| 23. C22×C8×C101 | C22 | semidirect |
| 27. #13108074 | C23 | semidirect |
| 32. C2×D404 | C23 | semidirect |
| 36. Dic404 | C23 | semidirect |
| 37. #13108063 | C23 | semidirect |
| 38. D808 | C23 | semidirect |
| 39. D808 | C23 | semidirect |
| 45. M16×C101 | C23 | semidirect |
| 48. C2×C8×C101 | C23 | semidirect |
| 80. C2×C101 | #576 | semidirect |
| 84. C101 | C2×#576 | semidirect |
| 90. C2×#131 | D101 | semidirect |
| 105. #131 | C2×D101 | semidirect |
| 106. C2×M16 | C2×D101 | semidirect |
| 107. C22×C8 | C2×D101 | semidirect |
| 129. M16 | C22×D101 | semidirect |
| 132. C2×C8 | C22×D101 | semidirect |
| 165. C2 | #20265982 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692301 | 2 |
| #20265982 | 2 |
| C2×#15692283 | 2 |
| C2×#15692277 | 2 |
| C22×D808 | 2 |
| C2×#131×C101 | 2 |
| C2×#576 | 101 |