Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#15692263 | C2 | semidirect |
| 3. #20265758 | C2 | semidirect |
| 4. #20265746 | C2 | semidirect |
| 5. #20265431 | C2 | semidirect |
| 6. #20265424 | C2 | semidirect |
| 7. #20265414 | C2 | semidirect |
| 8. #20265407 | C2 | semidirect |
| 9. #20265171 | C2 | semidirect |
| 10. C2×#15692175 | C2 | semidirect |
| 11. #428×C101 | C2 | semidirect |
| 19. C2×#13108057 | C22 | semidirect |
| 21. C2×C8×D101 | C22 | semidirect |
| 25. #15692235 | C22 | semidirect |
| 29. #15692230 | C22 | semidirect |
| 32. #15692178 | C22 | semidirect |
| 33. #15692178 | C22 | semidirect |
| 36. #15692175 | C22 | semidirect |
| 37. #15692175 | C22 | semidirect |
| 41. #107×C101 | C22 | semidirect |
| 42. #106×C101 | C22 | semidirect |
| 77. M16×C101 | D4 | semidirect |
| 152. C101 | #3062 | semidirect |
| 161. #428 | D101 | semidirect |
| 187. #107 | C2×D101 | semidirect |
| 188. #106 | C2×D101 | semidirect |
| 220. M16 | D404 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692283 | 2 |
| C2×#15692263 | 2 |
| #20265758 | 2 |
| #20265746 | 2 |
| #20265431 | 2 |
| #20265424 | 2 |
| #20265414 | 2 |
| #20265407 | 2 |
| #20265171 | 2 |
| C2×#15692175 | 2 |
| #428×C101 | 2 |
| #3062 | 101 |