Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
488 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 129 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. C2×C4×D668 | C2 | semidirect |
| 3. #24923588 | C2 | semidirect |
| 4. #24923560 | C2 | semidirect |
| 5. #24923465 | C2 | semidirect |
| 6. #24923405 | C2 | semidirect |
| 7. #24923382 | C2 | semidirect |
| 8. #432×C167 | C2 | semidirect |
| 13. #19128832 | C22 | semidirect |
| 14. #19128829 | C22 | semidirect |
| 23. C4×D668 | C22 | semidirect |
| 26. #19128764 | C22 | semidirect |
| 28. #19128754 | C22 | semidirect |
| 30. C4⋊C8×C167 | C22 | semidirect |
| 32. #97×C167 | C22 | semidirect |
| 76. D668 | #41 | semidirect |
| 120. C167 | #3109 | semidirect |
| 129. #432 | D167 | semidirect |
| 149. C4⋊C8 | C2×D167 | semidirect |
| 153. #97 | C2×D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923819 | 2 |
| C2×C4×D668 | 2 |
| #24923588 | 2 |
| #24923560 | 2 |
| #24923465 | 2 |
| #24923405 | 2 |
| #24923382 | 2 |
| #432×C167 | 2 |
| #3109 | 167 |