Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
792 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 269 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 |
|---|---|---|
| 2. C23×#11717579 | C2 | semidirect |
| 3. #20265171 | C2 | direct (N × H) |
| 4. C2×#15692178 | C2 | semidirect |
| 5. C2×#15692175 | C2 | semidirect |
| 6. C2×#117×C101 | C2 | semidirect |
| 9. C2×#13108074 | C4 | semidirect |
| 17. C22×#11717579 | C22 | semidirect |
| 18. #15692178 | C22 | semidirect |
| 19. #15692175 | C22 | semidirect |
| 22. #117×C101 | C22 | semidirect |
| 29. #13108074 | C2×C4 | semidirect |
| 103. C2×C101 | #416 | semidirect |
| 108. C101 | C2×#416 | semidirect |
| 111. C2×#117 | D101 | semidirect |
| 128. #117 | C2×D101 | semidirect |
| 212. C2 | #20265171 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13108074 | 2 |
| C23×#11717579 | 2 |
| #20265171 | 2 |
| C2×#15692178 | 2 |
| C2×#15692175 | 2 |
| C2×#117×C101 | 2 |
| C2×#416 | 101 |