Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
376 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 85 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×M16×D167 | C2 | semidirect |
| 3. C2×#19128760 | C2 | semidirect |
| 4. C2×#19128758 | C2 | semidirect |
| 5. C4×(C2×D167)⋊C4 | C2 | semidirect |
| 6. #24923028 | C2 | semidirect |
| 7. #339×C167 | C2 | semidirect |
| 16. #19128812 | C4 | semidirect |
| 17. #19128812 | C4 | semidirect |
| 18. #19128807 | C4 | semidirect |
| 19. #19128807 | C4 | semidirect |
| 53. #14581934 | D4 | semidirect |
| 69. M16×C167 | D4 | semidirect |
| 139. C2×D167 | #104 | semidirect |
| 159. C167 | #1871 | semidirect |
| 167. #339 | D167 | semidirect |
| 218. M16 | D668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×D167 | 2 |
| #24923781 | 2 |
| C2×#19128760 | 2 |
| C2×#19128758 | 2 |
| C4×(C2×D167)⋊C4 | 2 |
| #24923028 | 2 |
| #339×C167 | 2 |
| #1871 | 167 |