Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
520 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 157 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. #24923780 | C2 | semidirect |
| 3. #24923510 | C2 | semidirect |
| 4. #24923505 | C2 | semidirect |
| 5. #24923498 | C2 | semidirect |
| 6. #24923307 | C2 | semidirect |
| 7. #24923266 | C2 | semidirect |
| 8. C23×C8×C167 | C2 | semidirect |
| 11. C2×Dic668 | C22 | semidirect |
| 12. C2×#14581939 | C22 | semidirect |
| 13. C2×D1336 | C22 | semidirect |
| 20. #19128766 | C22 | semidirect |
| 21. #19128764 | C22 | semidirect |
| 22. #19128757 | C22 | semidirect |
| 23. #19128754 | C22 | semidirect |
| 56. C2×C8×C167 | D4 | semidirect |
| 91. C22×C167 | #135 | semidirect |
| 106. C167 | #3050 | semidirect |
| 109. C23×C8 | D167 | semidirect |
| 157. C2×C8 | C22⋊D167 | semidirect |
| 200. C22 | #19128854 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128854 | 2 |
| #24923780 | 2 |
| #24923510 | 2 |
| #24923505 | 2 |
| #24923498 | 2 |
| #24923307 | 2 |
| #24923266 | 2 |
| C23×C8×C167 | 2 |
| #3050 | 167 |