Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
410 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 3. #20265519 | C2 | semidirect |
| 4. #20265513 | C2 | semidirect |
| 5. #20265508 | C2 | semidirect |
| 6. #20265219 | C2 | semidirect |
| 7. #20265187 | C2 | semidirect |
| 25. #15692189 | C22 | semidirect |
| 26. #15692187 | C22 | semidirect |
| 27. #15692180 | C22 | semidirect |
| 28. #15692180 | C22 | semidirect |
| 117. C101 | #3095 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692234 | 2 |
| C2×#15692214 | 2 |
| #20265519 | 2 |
| #20265513 | 2 |
| #20265508 | 2 |
| #20265219 | 2 |
| #20265187 | 2 |
| #407×C101 | 2 |
| #3095 | 101 |