Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
196 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 66 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. #20266205 | C2 | semidirect |
| 2. #20266040 | C2 | semidirect |
| 3. #20266025 | C2 | semidirect |
| 4. C8×#11717581 | C2 | semidirect |
| 23. D808 | C8 | semidirect |
| 35. D404 | C2×C8 | semidirect |
| 41. #11717581 | D8 | semidirect |
| 42. C8×C101 | C2×C8 | semidirect |
| 59. C101 | C8×D8 | semidirect |
| 102. C8 | D101⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20266205 | 2 |
| #20266040 | 2 |
| #20266025 | 2 |
| C8×#11717581 | 2 |
| #20265259 | 2 |
| C8×D8 | 101 |