Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
700 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×#13108064 | C2 | semidirect |
| 3. #20265751 | C2 | semidirect |
| 4. #20265336 | C2 | semidirect |
| 5. #20265331 | C2 | semidirect |
| 6. #20265187 | C2 | semidirect |
| 7. #20265173 | C2 | semidirect |
| 8. #20265145 | C2 | semidirect |
| 9. C2×#137×C101 | C2 | semidirect |
| 141. C101 | #3011 | semidirect |
| 143. C2×#137 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692302 | 2 |
| C22×#13108064 | 2 |
| #20265751 | 2 |
| #20265336 | 2 |
| #20265331 | 2 |
| #20265187 | 2 |
| #20265173 | 2 |
| #20265145 | 2 |
| C2×#137×C101 | 2 |
| #3011 | 101 |