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×#19128862 | C2 | semidirect |
| 2. C2×#19128858 | C2 | semidirect |
| 3. C2×#19128852 | C2 | semidirect |
| 4. C22×#14581938 | C2 | semidirect |
| 5. #24923845 | C2 | semidirect |
| 6. #24923664 | C2 | semidirect |
| 7. #24923656 | C2 | semidirect |
| 8. #24923651 | C2 | semidirect |
| 9. #24923641 | C2 | semidirect |
| 10. #24923225 | C2 | semidirect |
| 11. #535×C167 | C2 | semidirect |
| 17. C2×#14581940 | C22 | semidirect |
| 18. C2×#14581940 | C22 | semidirect |
| 23. C2×#14581938 | C22 | semidirect |
| 24. C2×#14581938 | C22 | semidirect |
| 25. C2×#14581937 | C22 | semidirect |
| 27. C2×#14581935 | C22 | semidirect |
| 30. #19128832 | C22 | semidirect |
| 31. #19128820 | C22 | semidirect |
| 34. #19128743 | C22 | semidirect |
| 35. C4×C167⋊C8 | C22 | semidirect |
| 64. #14581934 | D4 | semidirect |
| 65. C2×C167⋊C8 | D4 | semidirect |
| 148. C167 | #3154 | semidirect |
| 155. #535 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128862 | 2 |
| C2×#19128858 | 2 |
| C2×#19128852 | 2 |
| C22×#14581938 | 2 |
| #24923845 | 2 |
| #24923664 | 2 |
| #24923656 | 2 |
| #24923651 | 2 |
| #24923641 | 2 |
| #24923225 | 2 |
| #535×C167 | 2 |
| #3154 | 167 |