Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
326 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 69 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. C2×#15692181 | C2 | semidirect |
| 3. #20265176 | C2 | semidirect |
| 4. C2×#15692171 | C2 | semidirect |
| 5. #20265078 | C2 | semidirect |
| 6. #20264936 | C2 | semidirect |
| 7. #428×C101 | C2 | semidirect |
| 56. M16×C101 | D4 | semidirect |
| 131. C101 | #2037 | semidirect |
| 133. #428 | D101 | semidirect |
| 181. M16 | D404 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265746 | 2 |
| C2×#15692181 | 2 |
| #20265176 | 2 |
| C2×#15692171 | 2 |
| #20265078 | 2 |
| #20264936 | 2 |
| #428×C101 | 2 |
| #2037 | 101 |