Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
524 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 141 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×#19128839 | C2 | semidirect |
| 3. #24923833 | C2 | semidirect |
| 4. #24923520 | C2 | semidirect |
| 5. #24923503 | C2 | semidirect |
| 6. #24923305 | C2 | semidirect |
| 7. #24923274 | C2 | semidirect |
| 8. #24923273 | C2 | semidirect |
| 9. #535×C167 | C2 | semidirect |
| 16. C2×#14581934 | C22 | semidirect |
| 18. C22×C167⋊C8 | C22 | semidirect |
| 21. #19128806 | C22 | semidirect |
| 24. #19128765 | C22 | semidirect |
| 25. #19128763 | C22 | semidirect |
| 26. #19128753 | C22 | semidirect |
| 27. #19128752 | C22 | semidirect |
| 32. #121×C167 | C22 | semidirect |
| 46. C2×C167⋊C8 | D4 | semidirect |
| 125. C167 | #3058 | semidirect |
| 130. #535 | D167 | semidirect |
| 152. #121 | 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×#19128839 | 2 |
| #24923833 | 2 |
| #24923520 | 2 |
| #24923503 | 2 |
| #24923305 | 2 |
| #24923274 | 2 |
| #24923273 | 2 |
| #535×C167 | 2 |
| #3058 | 167 |