Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
436 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 99 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. #24906073 | C2 | semidirect |
| 3. #24906024 | C2 | semidirect |
| 4. #24906001 | C2 | semidirect |
| 5. #24905363 | C2 | semidirect |
| 6. #24905345 | C2 | semidirect |
| 7. C83×#2968 | C2 | semidirect |
| 9. #19128111 | C4 | semidirect |
| 10. #19128091 | C4 | semidirect |
| 11. #19128067 | C4 | semidirect |
| 12. #19128060 | C4 | semidirect |
| 210. #2968 | 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 |
|---|---|
| #24918162 | 2 |
| #24906073 | 2 |
| #24906024 | 2 |
| #24906001 | 2 |
| #24905363 | 2 |
| #24905345 | 2 |
| C83×#2968 | 2 |
| #9432 | 83 |