Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
370 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 113 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. #20265978 | C2 | semidirect |
| 2. #20265613 | C2 | semidirect |
| 3. #20265611 | C2 | semidirect |
| 4. #20265609 | C2 | semidirect |
| 5. #20265606 | C2 | semidirect |
| 6. D16×D101 | C2 | semidirect |
| 7. #20265593 | C2 | semidirect |
| 8. C2×D16×C101 | C2 | semidirect |
| 12. #15692277 | C22 | semidirect |
| 13. #15692274 | C22 | semidirect |
| 14. D8×D101 | C22 | semidirect |
| 16. Dic808 | C22 | semidirect |
| 17. #15692200 | C22 | semidirect |
| 18. #15692199 | C22 | semidirect |
| 19. D1616 | C22 | semidirect |
| 20. #15692196 | C22 | semidirect |
| 21. #15692195 | C22 | semidirect |
| 22. #15692194 | C22 | semidirect |
| 23. C16×D101 | C22 | semidirect |
| 24. C2×D8×C101 | C22 | semidirect |
| 25. D16×C101 | C22 | semidirect |
| 26. D16×C101 | C22 | semidirect |
| 27. C2×C16×C101 | C22 | semidirect |
| 85. C101 | #3415 | semidirect |
| 92. C2×D16 | D101 | semidirect |
| 100. C2×D8 | C2×D101 | semidirect |
| 107. D16 | C2×D101 | semidirect |
| 108. D16 | C2×D101 | semidirect |
| 112. C2×C16 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265978 | 2 |
| #20265613 | 2 |
| #20265611 | 2 |
| #20265609 | 2 |
| #20265606 | 2 |
| D16×D101 | 2 |
| #20265593 | 2 |
| C2×D16×C101 | 2 |
| #3415 | 101 |