Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
272 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 13. Dic167⋊C8 | C4 | semidirect |
| 15. C8×Dic167 | C4 | semidirect |
| 65. C8×C167 | C4⋊C4 | semidirect |
| 78. Dic167 | #97 | semidirect |
| 84. C167 | #1770 | semidirect |
| 150. C8 | Dic167⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic167⋊C8 | 2 |
| C2×#19128742 | 2 |
| C2×C8×Dic167 | 2 |
| C4×Dic167⋊C4 | 2 |
| #24923024 | 2 |
| #24923023 | 2 |
| C2×#97×C167 | 2 |
| #1770 | 167 |