Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
162 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 2. C4×Dic404 | C2 | semidirect |
| 3. #20265004 | C2 | semidirect |
| 4. #20264980 | C2 | semidirect |
| 6. C4×#13108049 | C2 | semidirect |
| 10. #15692199 | C4 | direct (N × H) |
| 22. Dic404 | C2×C4 | semidirect |
| 27. #13108049 | C2×C4 | semidirect |
| 58. C4×C101 | SD32 | semidirect |
| 68. C101 | C4×SD32 | semidirect |
| 128. C4 | #15692199 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692199 | 2 |
| C4×Dic404 | 2 |
| #20265004 | 2 |
| #20264980 | 2 |
| #20264978 | 2 |
| C4×#13108049 | 2 |
| C4×D8×C101 | 2 |
| C4×SD32 | 101 |