Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
216 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 71 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. #20265225 | C2 | semidirect |
| 4. C4×#13108058 | C2 | semidirect |
| 5. #20264948 | C2 | semidirect |
| 6. #20264937 | C2 | semidirect |
| 14. #15692174 | C4 | semidirect |
| 15. #15692172 | C4 | semidirect |
| 96. C101 | #1932 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265225 | 2 |
| #20265194 | 2 |
| #20265161 | 2 |
| C4×#13108058 | 2 |
| #20264948 | 2 |
| #20264937 | 2 |
| C2×#104×C101 | 2 |
| #1932 | 101 |