Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
260 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 34. #13095495 | Q8 | semidirect |
| 50. M16×C97 | Q8 | semidirect |
| 99. C97 | #1997 | semidirect |
| 139. M16 | Dic194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690809 | 2 |
| #20260758 | 2 |
| M16×Dic97 | 2 |
| #20260504 | 2 |
| #20260503 | 2 |
| #343×C97 | 2 |
| #1997 | 97 |