Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
500 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 229 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 |
|---|---|---|
| 10. C4×Dic194 | C4 | semidirect |
| 46. C42×C97 | Q8 | semidirect |
| 88. C97 | #2295 | semidirect |
| 133. C42 | Dic194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic194 | 2 |
| #20260641 | 2 |
| #20260633 | 2 |
| #20260619 | 2 |
| C4×#13095490 | 2 |
| C4×C4⋊Dic97 | 2 |
| #20260581 | 2 |
| C43×C97 | 2 |
| #2295 | 97 |