Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
612 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 205 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. C2×C4×Dic334 | C2 | semidirect |
| 3. #24923174 | C2 | semidirect |
| 5. #24923157 | C2 | semidirect |
| 6. #24923142 | C2 | semidirect |
| 7. #24923138 | C2 | semidirect |
| 8. #24923115 | C2 | semidirect |
| 11. #19128819 | C4 | semidirect |
| 32. C2×Dic334 | C2×C4 | semidirect |
| 41. C22⋊Dic167 | C2×C4 | semidirect |
| 44. C4×Dic167 | C2×C4 | semidirect |
| 111. C167 | #2326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128819 | 2 |
| C2×C4×Dic334 | 2 |
| #24923174 | 2 |
| #24923172 | 2 |
| #24923157 | 2 |
| #24923142 | 2 |
| #24923138 | 2 |
| #24923115 | 2 |
| C2×C4×D4×C167 | 2 |
| #2326 | 167 |