Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
418 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 1. #24909686 | C2 | semidirect |
| 2. #24909610 | C2 | semidirect |
| 3. #24906862 | C2 | semidirect |
| 4. #24905509 | C2 | semidirect |
| 5. #24905424 | C2 | semidirect |
| 6. D4⋊(C83⋊C16) | C2 | semidirect |
| 8. #19128106 | C22 | semidirect |
| 11. C4⋊(C83⋊C16) | C22 | semidirect |
| 14. C4×C83⋊C16 | C22 | semidirect |
| 15. #19127454 | C22 | semidirect |
| 157. C83 | #12372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909686 | 2 |
| #24909610 | 2 |
| #24906862 | 2 |
| #24905509 | 2 |
| #24905424 | 2 |
| D4⋊(C83⋊C16) | 2 |
| D4×D8×C83 | 2 |
| #12372 | 83 |