Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
230 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 19. #15692187 | C4 | semidirect |
| 20. #15692186 | C4 | semidirect |
| 21. #15692186 | C4 | semidirect |
| 22. #106×C101 | C4 | semidirect |
| 108. C101 | #1920 | semidirect |
| 128. #106 | #87938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20266128 | 2 |
| C4⋊C4×#87938 | 2 |
| #20266051 | 2 |
| #20266050 | 2 |
| (C2×#87938)⋊C8 | 2 |
| #106×D101 | 2 |
| #1920 | 101 |