Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 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×#15692277 | C2 | semidirect |
| 2. C22×#13108057 | C2 | semidirect |
| 3. #20265689 | C2 | semidirect |
| 4. #20265436 | C2 | semidirect |
| 5. #20265431 | C2 | semidirect |
| 6. #20265424 | C2 | semidirect |
| 7. #20265171 | C2 | semidirect |
| 8. #427×C101 | C2 | semidirect |
| 12. C2×Dic404 | C22 | semidirect |
| 13. C2×#13108063 | C22 | semidirect |
| 14. C2×D808 | C22 | semidirect |
| 24. #15692178 | C22 | semidirect |
| 25. #15692175 | C22 | semidirect |
| 28. #107×C101 | C22 | semidirect |
| 29. #106×C101 | C22 | semidirect |
| 54. C2×C8×C101 | D4 | semidirect |
| 106. C101 | #3054 | semidirect |
| 113. #427 | D101 | semidirect |
| 132. #107 | C2×D101 | semidirect |
| 133. #106 | C2×D101 | semidirect |
| 157. C2×C8 | D404 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692277 | 2 |
| C22×#13108057 | 2 |
| #20265689 | 2 |
| #20265436 | 2 |
| #20265431 | 2 |
| #20265424 | 2 |
| #20265171 | 2 |
| #427×C101 | 2 |
| #3054 | 101 |