Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
552 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 221 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 |
|---|---|---|
| 2. #24923162 | C2 | semidirect |
| 3. #24923162 | C2 | semidirect |
| 4. #24923155 | C2 | semidirect |
| 6. C4⋊C4×Dic167 | C2 | semidirect |
| 7. C22⋊C4×Dic167 | C2 | semidirect |
| 8. C4×C22⋊Dic167 | C2 | semidirect |
| 28. #123×C167 | C4 | semidirect |
| 55. C22×C4×C167 | C2×C4 | semidirect |
| 59. C4⋊C4×C167 | C2×C4 | semidirect |
| 61. C22⋊C4×C167 | C2×C4 | semidirect |
| 126. C167 | #2374 | semidirect |
| 140. #123 | Dic167 | semidirect |
| 172. C22×C4 | C2×Dic167 | semidirect |
| 178. C4⋊C4 | C2×Dic167 | semidirect |
| 184. C22⋊C4 | C2×Dic167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923172 | 2 |
| #24923162 | 2 |
| #24923155 | 2 |
| #24923149 | 2 |
| C4⋊C4×Dic167 | 2 |
| C22⋊C4×Dic167 | 2 |
| C4×C22⋊Dic167 | 2 |
| C2×#123×C167 | 2 |
| #2374 | 167 |