Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
364 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 364 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. C2×#19128854 | C2 | semidirect |
| 2. #24923710 | C2 | semidirect |
| 3. #24923709 | C2 | semidirect |
| 4. #24923705 | C2 | semidirect |
| 5. #24923704 | C2 | semidirect |
| 6. #24923699 | C2 | semidirect |
| 7. C2×#19128772 | C2 | semidirect |
| 8. C2×#135×C167 | C2 | semidirect |
| 13. #19128854 | C22 | semidirect |
| 14. C2×Dic668 | C22 | semidirect |
| 16. C2×D1336 | C22 | semidirect |
| 17. #19128778 | C22 | semidirect |
| 18. #19128776 | C22 | semidirect |
| 19. #19128775 | C22 | semidirect |
| 20. #19128773 | C22 | semidirect |
| 21. #19128772 | C22 | semidirect |
| 22. #19128772 | C22 | semidirect |
| 23. C2×C167⋊C16 | C22 | semidirect |
| 28. #135×C167 | C22 | semidirect |
| 29. C2×Q16×C167 | C22 | semidirect |
| 31. C2×D8×C167 | C22 | semidirect |
| 120. C167 | #3414 | semidirect |
| 123. C2×#135 | D167 | semidirect |
| 139. #135 | C2×D167 | semidirect |
| 141. C2×Q16 | C2×D167 | semidirect |
| 145. C2×D8 | C2×D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128854 | 2 |
| #24923710 | 2 |
| #24923709 | 2 |
| #24923705 | 2 |
| #24923704 | 2 |
| #24923699 | 2 |
| C2×#19128772 | 2 |
| C2×#135×C167 | 2 |
| #3414 | 167 |