Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
384 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×C4×C167⋊C8 | C2 | semidirect |
| 4. C2×C8×Dic167 | C2 | semidirect |
| 6. #24923023 | C2 | semidirect |
| 7. #336×C167 | C2 | semidirect |
| 13. C2×C8×D167 | C4 | semidirect |
| 16. (C2×D167)⋊C8 | C4 | semidirect |
| 39. (C2×D167)⋊C4 | C8 | semidirect |
| 62. C2×Dic167 | C2×C8 | semidirect |
| 68. C167⋊C8 | C22⋊C4 | semidirect |
| 72. C2×C4×C167 | C2×C8 | semidirect |
| 90. C2×D167 | C4×C8 | semidirect |
| 104. C167 | C8×C22⋊C4 | semidirect |
| 112. #336 | D167 | semidirect |
| 175. C2×C4 | C8×D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D167 | 2 |
| C2×(C2×D167)⋊C8 | 2 |
| C2×C4×C167⋊C8 | 2 |
| C2×C8×Dic167 | 2 |
| C4×(C2×D167)⋊C4 | 2 |
| #24923023 | 2 |
| #336×C167 | 2 |
| C8×C22⋊C4 | 167 |