Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
436 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 436 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. #24916457 | C2 | semidirect |
| 3. #24906073 | C2 | semidirect |
| 4. #24906022 | C2 | semidirect |
| 5. #24905999 | C2 | semidirect |
| 6. #24905362 | C2 | semidirect |
| 7. C83×#1295 | C2 | semidirect |
| 10. #19128110 | C4 | semidirect |
| 11. #19128090 | C4 | semidirect |
| 12. #19128066 | C4 | semidirect |
| 13. #19128061 | C4 | semidirect |
| 215. #1295 | D83 | semidirect |
| 216. C83 | #9432 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918161 | 2 |
| #24916457 | 2 |
| #24906073 | 2 |
| #24906022 | 2 |
| #24905999 | 2 |
| #24905362 | 2 |
| C83×#1295 | 2 |
| #9432 | 83 |