Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
552 conjugacy classes of subgroups; only the 275 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 275 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 |
|---|---|---|
| 9. Q8×Dic167 | C4 | semidirect |
| 54. Q8×C167 | C4⋊C4 | semidirect |
| 85. C167 | #2351 | semidirect |
| 128. Q8 | Dic167⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×Dic167 | 2 |
| #24923167 | 2 |
| #24923165 | 2 |
| #24923134 | 2 |
| C4×Dic167⋊C4 | 2 |
| C2×C4×Q8×C167 | 2 |
| #2351 | 167 |