Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
240 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 21. C4⋊#11717579 | C4 | semidirect |
| 22. #15692184 | C4 | semidirect |
| 23. #15692184 | C4 | semidirect |
| 24. C4⋊C8×C101 | C4 | semidirect |
| 111. C101 | #1949 | semidirect |
| 132. C4⋊C8 | #87938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692324 | 2 |
| C2×#15692323 | 2 |
| #20266121 | 2 |
| C4×C4⋊#87938 | 2 |
| #20266051 | 2 |
| C4⋊C8×D101 | 2 |
| #1949 | 101 |