Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
274 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
| 2. #20265194 | C2 | semidirect |
| 3. #20265182 | C2 | semidirect |
| 4. #20265161 | C2 | semidirect |
| 5. C2×#15692172 | C2 | semidirect |
| 6. #20264949 | C2 | semidirect |
| 111. C101 | #2048 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265225 | 2 |
| #20265194 | 2 |
| #20265182 | 2 |
| #20265161 | 2 |
| C2×#15692172 | 2 |
| #20264949 | 2 |
| C2×AGL(1,ℤ/8)×C101 | 2 |
| #2048 | 101 |