Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
184 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 3. #20260510 | C2 | semidirect |
| 4. C16×Dic97 | C2 | semidirect |
| 8. C2×#13095486 | C4 | semidirect |
| 14. M32×C97 | C4 | semidirect |
| 50. C97 | #2108 | semidirect |
| 59. M32 | Dic97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095486 | 2 |
| #20260690 | 2 |
| #20260510 | 2 |
| C16×Dic97 | 2 |
| C2×M32×C97 | 2 |
| #2108 | 97 |