Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
126 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 22. #13095523 | Q8 | semidirect |
| 60. C97 | #2183 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261838 | 2 |
| C4⋊#13095523 | 2 |
| #20261829 | 2 |
| C4×#13095523 | 2 |
| #20261784 | 2 |
| #2183 | 97 |