Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
650 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 2. #24908381 | C2 | semidirect |
| 3. #24905970 | C2 | semidirect |
| 4. #24905906 | C2 | semidirect |
| 5. #24905356 | C2 | semidirect |
| 6. #24905319 | C2 | semidirect |
| 7. C83×#2275 | C2 | semidirect |
| 10. #19127991 | C4 | semidirect |
| 11. #19127896 | C4 | semidirect |
| 32. #14581792 | C2×C4 | semidirect |
| 33. #14581789 | C2×C4 | semidirect |
| 41. C4⋊(C83⋊C8) | C2×C4 | semidirect |
| 129. D4×C83 | #104 | semidirect |
| 198. #2275 | D83 | semidirect |
| 204. C83 | #9325 | semidirect |
| 332. D4 | #14581720 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917554 | 2 |
| #24908381 | 2 |
| #24905970 | 2 |
| #24905906 | 2 |
| #24905356 | 2 |
| #24905319 | 2 |
| C83×#2275 | 2 |
| #9325 | 83 |