Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
464 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 85 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. #24916523 | C2 | semidirect |
| 3. #24906017 | C2 | semidirect |
| 4. #24905823 | C2 | semidirect |
| 5. #24905371 | C2 | semidirect |
| 6. #24905339 | C2 | semidirect |
| 7. C83×#1510 | C2 | semidirect |
| 9. #19128031 | C4 | semidirect |
| 11. #19128014 | C4 | semidirect |
| 14. #19127852 | C4 | semidirect |
| 16. #19127835 | C4 | semidirect |
| 229. #1510 | D83 | semidirect |
| 233. C83 | #9332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918277 | 2 |
| #24916523 | 2 |
| #24906017 | 2 |
| #24905823 | 2 |
| #24905371 | 2 |
| #24905339 | 2 |
| C83×#1510 | 2 |
| #9332 | 83 |