Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
350 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 113 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. #20265991 | C2 | semidirect |
| 2. #20265990 | C2 | semidirect |
| 3. #20265620 | C2 | semidirect |
| 4. #20265619 | C2 | semidirect |
| 5. #20265616 | C2 | semidirect |
| 6. #20265608 | C2 | semidirect |
| 7. #20265607 | C2 | semidirect |
| 8. C2×#15692201 | C2 | semidirect |
| 9. Q32×D101 | C2 | semidirect |
| 10. #20265595 | C2 | semidirect |
| 11. #510×C101 | C2 | semidirect |
| 124. C101 | #3417 | semidirect |
| 130. #510 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265991 | 2 |
| #20265990 | 2 |
| #20265620 | 2 |
| #20265619 | 2 |
| #20265616 | 2 |
| #20265608 | 2 |
| #20265607 | 2 |
| C2×#15692201 | 2 |
| Q32×D101 | 2 |
| #20265595 | 2 |
| #510×C101 | 2 |
| #3417 | 101 |