Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#15692261 | C2 | semidirect |
| 2. #20265751 | C2 | semidirect |
| 4. #20265420 | C2 | semidirect |
| 5. #20265403 | C2 | semidirect |
| 6. #20265215 | C2 | semidirect |
| 7. #20265186 | C2 | semidirect |
| 8. #20265182 | C2 | semidirect |
| 9. C22×SD16×C101 | C2 | semidirect |
| 13. C2×#13108057 | C22 | semidirect |
| 14. C2×C8×D101 | C22 | semidirect |
| 20. #15692231 | C22 | semidirect |
| 25. #15692189 | C22 | semidirect |
| 26. #15692187 | C22 | semidirect |
| 27. #15692179 | C22 | semidirect |
| 68. C2×C8×C101 | D4 | semidirect |
| 121. C101 | #3057 | semidirect |
| 122. C22×SD16 | D101 | semidirect |
| 180. C2×C8 | C22⋊D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692261 | 2 |
| #20265751 | 2 |
| #20265744 | 2 |
| #20265420 | 2 |
| #20265403 | 2 |
| #20265215 | 2 |
| #20265186 | 2 |
| #20265182 | 2 |
| C22×SD16×C101 | 2 |
| #3057 | 101 |