Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
336 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 336 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 |
|---|---|---|
| 77. Dic334 | Q16 | semidirect |
| 112. C167 | #3363 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic334 | 2 |
| #24923997 | 2 |
| #24923620 | 2 |
| #24923618 | 2 |
| #24923564 | 2 |
| #24923563 | 2 |
| #24923479 | 2 |
| #24923477 | 2 |
| C8×Dic334 | 2 |
| #24923361 | 2 |
| C4×Q16×C167 | 2 |
| #3363 | 167 |