Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
160 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 25. Dic388 | C8 | semidirect |
| 26. #13095501 | C8 | semidirect |
| 28. Q16×C97 | C8 | semidirect |
| 55. C97 | #1579 | semidirect |
| 74. Q16 | #11715906 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11715906 | 2 |
| #20261824 | 2 |
| Q8⋊#11715906 | 2 |
| #20261819 | 2 |
| Q16×#87604 | 2 |
| #1579 | 97 |