Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
356 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 166 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 |
|---|---|---|
| 1. #20261786 | C2 | semidirect |
| 2. #20261785 | C2 | semidirect |
| 3. #20261784 | C2 | semidirect |
| 31. #13095521 | Q8 | semidirect |
| 91. C97 | #2962 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261786 | 2 |
| #20261785 | 2 |
| #20261784 | 2 |
| #20261742 | 2 |
| #20261736 | 2 |
| #20261700 | 2 |
| C4×#13095521 | 2 |
| #20261290 | 2 |
| #2962 | 97 |