Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
632 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 109 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. #24910188 | C2 | semidirect |
| 3. #24908295 | C2 | semidirect |
| 4. #24906130 | C2 | semidirect |
| 5. #24906024 | C2 | semidirect |
| 6. #24905322 | C2 | semidirect |
| 7. C83×#1274 | C2 | semidirect |
| 11. #19128078 | C4 | semidirect |
| 12. #19128048 | C4 | semidirect |
| 34. #14581792 | C2×C4 | semidirect |
| 38. #14581789 | C2×C4 | semidirect |
| 66. C4×C8×C83 | C2×C4 | semidirect |
| 119. C42×C83 | D8 | semidirect |
| 218. #1274 | D83 | semidirect |
| 219. C83 | #9299 | semidirect |
| 276. C4×C8 | C4×D83 | semidirect |
| 331. C42 | D664 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918383 | 2 |
| #24910188 | 2 |
| #24908295 | 2 |
| #24906130 | 2 |
| #24906024 | 2 |
| #24905322 | 2 |
| C83×#1274 | 2 |
| #9299 | 83 |