Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
160 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 64 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 |
|---|---|---|
| 29. #13095501 | C8 | semidirect |
| 72. C97 | #1579 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261784 | 2 |
| Q8×#11715897 | 2 |
| #20261597 | 2 |
| #20261585 | 2 |
| Q8⋊#11715897 | 2 |
| #20261576 | 2 |
| #20260827 | 2 |
| #1579 | 97 |