Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
196 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 129 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. #20260510 | C2 | semidirect |
| 4. C16×Dic97 | C2 | semidirect |
| 8. #15690750 | C4 | semidirect |
| 15. M32×C97 | C4 | semidirect |
| 24. #13095486 | C2×C4 | semidirect |
| 30. C16×C97 | C2×C4 | semidirect |
| 51. Dic97 | M32 | direct (N × H) |
| 56. C97 | C4×M32 | semidirect |
| 66. M32 | Dic97 | direct (N × H) |
| 86. C16 | C2×Dic97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690750 | 2 |
| C2×C8×Dic97 | 2 |
| #20260510 | 2 |
| C16×Dic97 | 2 |
| C2×M32×C97 | 2 |
| C4×M32 | 97 |