Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
552 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 153 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 |
|---|---|---|
| 1. C2×#19128865 | C2 | semidirect |
| 2. C2×#19128863 | C2 | semidirect |
| 3. C2×#19128862 | C2 | semidirect |
| 5. C2×#19128830 | C2 | semidirect |
| 6. #24923662 | C2 | semidirect |
| 7. #24923660 | C2 | semidirect |
| 8. #24923647 | C2 | semidirect |
| 9. #24923640 | C2 | semidirect |
| 10. M16×Dic167 | C2 | semidirect |
| 11. C2×#137×C167 | C2 | semidirect |
| 62. #14581934 | D4 | semidirect |
| 86. M16×C167 | D4 | semidirect |
| 140. Dic167 | #137 | semidirect |
| 146. C167 | #3152 | semidirect |
| 151. C2×#137 | D167 | semidirect |
| 224. M16 | C22⋊D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128865 | 2 |
| C2×#19128863 | 2 |
| C2×#19128862 | 2 |
| #24923815 | 2 |
| C2×#19128830 | 2 |
| #24923662 | 2 |
| #24923660 | 2 |
| #24923647 | 2 |
| #24923640 | 2 |
| M16×Dic167 | 2 |
| C2×#137×C167 | 2 |
| #3152 | 167 |