Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 416 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 |
|---|---|---|
| 3. #20265519 | C2 | direct (N × H) |
| 4. C2×#15692189 | C2 | semidirect |
| 5. C2×#15692187 | C2 | semidirect |
| 6. C2×#15692180 | C2 | semidirect |
| 7. C2×#15692180 | C2 | semidirect |
| 21. #15692189 | C22 | semidirect |
| 22. #15692187 | C22 | semidirect |
| 23. #15692180 | C22 | semidirect |
| 24. #15692180 | C22 | semidirect |
| 102. C2×C101 | #485 | semidirect |
| 107. C101 | C2×#485 | semidirect |
| 209. C2 | #20265519 | direct (N × H) |
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 |
| C2×#15692189 | 2 |
| C2×#15692187 | 2 |
| C2×#15692180 | 2 |
| C2×C22⋊C8×C101 | 2 |
| C2×#485 | 101 |