Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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×#19128863 | C2 | semidirect |
| 2. C2×#19128858 | C2 | semidirect |
| 3. C2×#19128854 | C2 | semidirect |
| 4. #24923843 | C2 | semidirect |
| 5. #24923836 | C2 | semidirect |
| 6. #24923660 | C2 | semidirect |
| 7. #24923655 | C2 | semidirect |
| 8. #24923650 | C2 | semidirect |
| 9. #24923640 | C2 | semidirect |
| 10. #24923224 | C2 | semidirect |
| 11. C22×SD16×C167 | C2 | semidirect |
| 17. C2×Dic668 | C22 | semidirect |
| 18. C2×#14581940 | C22 | semidirect |
| 19. C2×#14581939 | C22 | semidirect |
| 20. C2×#14581939 | C22 | semidirect |
| 22. C2×#14581937 | C22 | semidirect |
| 23. C2×D1336 | C22 | semidirect |
| 26. #19128830 | C22 | semidirect |
| 28. #19128821 | C22 | semidirect |
| 35. #19128742 | C22 | semidirect |
| 36. C8×Dic167 | C22 | semidirect |
| 64. #14581934 | D4 | semidirect |
| 85. C2×C8×C167 | D4 | semidirect |
| 148. C167 | #3154 | semidirect |
| 153. C22×SD16 | D167 | semidirect |
| 228. C2×C8 | C22⋊D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128863 | 2 |
| C2×#19128858 | 2 |
| C2×#19128854 | 2 |
| #24923843 | 2 |
| #24923836 | 2 |
| #24923660 | 2 |
| #24923655 | 2 |
| #24923650 | 2 |
| #24923640 | 2 |
| #24923224 | 2 |
| C22×SD16×C167 | 2 |
| #3154 | 167 |