Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
504 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 93 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. #20260501 | C2 | semidirect |
| 5. C23×Dic97 | C4 | semidirect |
| 9. C2×C22⋊Dic97 | C4 | semidirect |
| 90. C97 | #1819 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊Dic97 | 2 |
| #20260591 | 2 |
| #20260501 | 2 |
| #379×C97 | 2 |
| #1819 | 97 |