Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
526 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 149 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×#15692281 | C2 | semidirect |
| 2. C22×#13108059 | C2 | semidirect |
| 3. #20265746 | C2 | semidirect |
| 4. #20265392 | C2 | semidirect |
| 5. #20265372 | C2 | semidirect |
| 6. #20265204 | C2 | semidirect |
| 7. #20265181 | C2 | semidirect |
| 8. #20265171 | C2 | semidirect |
| 9. #518×C101 | C2 | semidirect |
| 13. C2×#13108062 | C22 | semidirect |
| 16. C2×#13108059 | C22 | semidirect |
| 19. #15692252 | C22 | semidirect |
| 20. #15692243 | C22 | semidirect |
| 23. C4⋊#11717579 | C22 | semidirect |
| 24. #15692178 | C22 | semidirect |
| 25. #15692175 | C22 | semidirect |
| 26. #15692175 | C22 | semidirect |
| 29. C4×D4×C101 | C22 | semidirect |
| 56. C2×D4×C101 | D4 | semidirect |
| 122. C101 | #3041 | semidirect |
| 126. #518 | D101 | semidirect |
| 147. C4×D4 | C2×D101 | semidirect |
| 169. C2×D4 | D404 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692281 | 2 |
| C22×#13108059 | 2 |
| #20265746 | 2 |
| #20265392 | 2 |
| #20265372 | 2 |
| #20265204 | 2 |
| #20265181 | 2 |
| #20265171 | 2 |
| #518×C101 | 2 |
| #3041 | 101 |