Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
372 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 71 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. #24909699 | C2 | semidirect |
| 2. #24909610 | C2 | semidirect |
| 3. #24906976 | C2 | semidirect |
| 4. #24905506 | C2 | semidirect |
| 5. #24905430 | C2 | semidirect |
| 6. #24905421 | C2 | semidirect |
| 8. #19128106 | C22 | semidirect |
| 11. C4⋊(C83⋊C16) | C22 | semidirect |
| 15. #19127477 | C22 | semidirect |
| 16. #19127452 | C22 | semidirect |
| 91. D8×C83 | SD16 | semidirect |
| 174. C83 | #12378 | semidirect |
| 253. D8 | #13050578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909699 | 2 |
| #24909610 | 2 |
| #24906976 | 2 |
| #24905506 | 2 |
| #24905430 | 2 |
| #24905421 | 2 |
| C83×#3273 | 2 |
| #12378 | 83 |