Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
328 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 3. C2×#19127479 | C2 | semidirect |
| 5. #24905571 | C2 | semidirect |
| 6. #24905561 | C2 | semidirect |
| 7. C83×#1943 | C2 | semidirect |
| 15. #19127504 | C4 | semidirect |
| 16. #19127501 | C4 | semidirect |
| 153. #1943 | D83 | semidirect |
| 156. C83 | #13153 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19127510 | 2 |
| #24909173 | 2 |
| C2×#19127479 | 2 |
| #24908356 | 2 |
| #24905571 | 2 |
| #24905561 | 2 |
| C83×#1943 | 2 |
| #13153 | 83 |