Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
168 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 81 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. #20260487 | C2 | semidirect |
| 4. #20260485 | C2 | semidirect |
| 67. C97 | #1568 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20260792 | 2 |
| C2×C4×#11715895 | 2 |
| #20260487 | 2 |
| #20260485 | 2 |
| #432×C97 | 2 |
| #1568 | 97 |