Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
196 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 97 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. #20261830 | C2 | semidirect |
| 3. #20261828 | C2 | semidirect |
| 5. #15690907 | C4 | semidirect |
| 6. #15690906 | C4 | semidirect |
| 15. #13095523 | C2×C4 | semidirect |
| 52. #87604 | M32 | semidirect |
| 62. C97 | C4×M32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261854 | 2 |
| #20261830 | 2 |
| #20261828 | 2 |
| C2×C8×#87604 | 2 |
| C4×M32 | 97 |