Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
348 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 80. Dic334 | Q16 | semidirect |
| 115. C167 | #3395 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923997 | 2 |
| #24923994 | 2 |
| #24923648 | 2 |
| #24923647 | 2 |
| #24923480 | 2 |
| #24923478 | 2 |
| #24923477 | 2 |
| #24923393 | 2 |
| C4×#14581940 | 2 |
| #24923361 | 2 |
| #462×C167 | 2 |
| #3395 | 167 |