Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
524 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 133 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. C22×#14581935 | C2 | semidirect |
| 2. C2×#19128840 | C2 | semidirect |
| 3. #24923838 | C2 | semidirect |
| 4. #24923836 | C2 | semidirect |
| 5. #24923521 | C2 | semidirect |
| 6. #24923504 | C2 | semidirect |
| 7. #24923305 | C2 | semidirect |
| 8. #24923275 | C2 | semidirect |
| 9. #418×C167 | C2 | semidirect |
| 16. C2×#14581933 | C22 | semidirect |
| 18. C2×C8×D167 | C22 | semidirect |
| 23. #19128807 | C22 | semidirect |
| 24. #19128803 | C22 | semidirect |
| 28. #19128765 | C22 | semidirect |
| 29. #19128763 | C22 | semidirect |
| 30. #19128754 | C22 | semidirect |
| 34. #102×C167 | C22 | semidirect |
| 51. C2×C167⋊C8 | D4 | semidirect |
| 125. C167 | #3058 | semidirect |
| 135. #418 | D167 | semidirect |
| 160. #102 | C2×D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14581935 | 2 |
| C2×#19128840 | 2 |
| #24923838 | 2 |
| #24923836 | 2 |
| #24923521 | 2 |
| #24923504 | 2 |
| #24923305 | 2 |
| #24923275 | 2 |
| #418×C167 | 2 |
| #3058 | 167 |