Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
488 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 133 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. #24923819 | C2 | semidirect |
| 2. #24923587 | C2 | semidirect |
| 3. #24923559 | C2 | semidirect |
| 4. #24923464 | C2 | semidirect |
| 5. #24923403 | C2 | semidirect |
| 6. #24923379 | C2 | semidirect |
| 7. #24923326 | C2 | semidirect |
| 8. C2×C4×D4×C167 | C2 | semidirect |
| 11. #19128832 | C22 | semidirect |
| 12. #19128829 | C22 | semidirect |
| 17. C4×D668 | C22 | semidirect |
| 18. #19128763 | C22 | semidirect |
| 19. C4⋊(C167⋊C8) | C22 | semidirect |
| 21. #19128752 | C22 | semidirect |
| 23. #19128743 | C22 | semidirect |
| 81. D4×C167 | #41 | semidirect |
| 120. C167 | #3109 | semidirect |
| 123. C2×C4×D4 | D167 | semidirect |
| 199. D4 | #14581950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923819 | 2 |
| #24923587 | 2 |
| #24923559 | 2 |
| #24923464 | 2 |
| #24923403 | 2 |
| #24923379 | 2 |
| #24923326 | 2 |
| C2×C4×D4×C167 | 2 |
| #3109 | 167 |