Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
206 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 51. Dic334 | Q16 | semidirect |
| 59. Q8×C167 | Q16 | semidirect |
| 82. C167 | #1633 | semidirect |
| 137. Q8 | #14581940 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic334 | 2 |
| #24923648 | 2 |
| #24923561 | 2 |
| #24923017 | 2 |
| Q8⋊(C167⋊C8) | 2 |
| #24922999 | 2 |
| #477×C167 | 2 |
| #1633 | 167 |