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. C2×#15692286 | C2 | semidirect |
| 3. C22×#13108064 | C2 | semidirect |
| 4. #20265337 | C2 | semidirect |
| 5. #20265332 | C2 | semidirect |
| 6. #20265185 | C2 | semidirect |
| 7. #20265171 | C2 | semidirect |
| 8. #20265144 | C2 | semidirect |
| 9. #536×C101 | C2 | semidirect |
| 141. C101 | #3011 | semidirect |
| 145. #536 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692302 | 2 |
| C2×#15692286 | 2 |
| C22×#13108064 | 2 |
| #20265337 | 2 |
| #20265332 | 2 |
| #20265185 | 2 |
| #20265171 | 2 |
| #20265144 | 2 |
| #536×C101 | 2 |
| #3011 | 101 |