Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
456 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 89 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. #24916538 | C2 | semidirect |
| 3. #24905970 | C2 | semidirect |
| 4. #24905970 | C2 | semidirect |
| 5. #24905933 | C2 | semidirect |
| 6. #24905325 | C2 | semidirect |
| 7. C83×#1274 | C2 | semidirect |
| 10. #19128078 | C4 | semidirect |
| 11. #19128074 | C4 | semidirect |
| 12. #19128052 | C4 | semidirect |
| 13. #19128048 | C4 | semidirect |
| 185. #1274 | D83 | semidirect |
| 186. C83 | #9281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918398 | 2 |
| #24916538 | 2 |
| #24905970 | 2 |
| #24905933 | 2 |
| #24905325 | 2 |
| C83×#1274 | 2 |
| #9281 | 83 |