Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
504 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 504 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×#15692283 | C2 | semidirect |
| 2. #20265755 | C2 | semidirect |
| 3. #20265741 | C2 | semidirect |
| 4. #20265430 | C2 | semidirect |
| 5. #20265423 | C2 | semidirect |
| 6. #20265413 | C2 | semidirect |
| 7. #20265406 | C2 | semidirect |
| 8. #20265219 | C2 | semidirect |
| 9. #20265174 | C2 | semidirect |
| 10. C2×#15692177 | C2 | semidirect |
| 11. C2×#131×C101 | C2 | semidirect |
| 19. #15692234 | C22 | semidirect |
| 23. #15692229 | C22 | semidirect |
| 29. #15692189 | C22 | semidirect |
| 30. #15692187 | C22 | semidirect |
| 31. #15692180 | C22 | semidirect |
| 32. #15692180 | C22 | semidirect |
| 35. #15692177 | C22 | semidirect |
| 36. #15692177 | C22 | semidirect |
| 40. C2×M16×C101 | C22 | semidirect |
| 42. C22×C8×C101 | C22 | semidirect |
| 79. M16×C101 | D4 | semidirect |
| 152. C101 | #3062 | semidirect |
| 154. C2×#131 | D101 | semidirect |
| 172. C2×M16 | C2×D101 | semidirect |
| 174. C22×C8 | C2×D101 | semidirect |
| 220. M16 | C22⋊D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692283 | 2 |
| #20265755 | 2 |
| #20265741 | 2 |
| #20265430 | 2 |
| #20265423 | 2 |
| #20265413 | 2 |
| #20265406 | 2 |
| #20265219 | 2 |
| #20265174 | 2 |
| C2×#15692177 | 2 |
| C2×#131×C101 | 2 |
| #3062 | 101 |