Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
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×Dic388 | C2 | semidirect |
| 3. #20260562 | C2 | semidirect |
| 4. #20260538 | C2 | semidirect |
| 6. C4×#13095486 | C2 | semidirect |
| 10. #15690754 | C4 | direct (N × H) |
| 22. Dic388 | C2×C4 | semidirect |
| 27. #13095486 | C2×C4 | semidirect |
| 58. C4×C97 | SD32 | semidirect |
| 68. C97 | C4×SD32 | semidirect |
| 128. C4 | #15690754 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690754 | 2 |
| C4×Dic388 | 2 |
| #20260562 | 2 |
| #20260538 | 2 |
| #20260536 | 2 |
| C4×#13095486 | 2 |
| C4×D8×C97 | 2 |
| C4×SD32 | 97 |