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 |
|---|---|---|
| 2. C2×#19127478 | C2 | semidirect |
| 4. #24908199 | C2 | semidirect |
| 5. #24905572 | C2 | semidirect |
| 6. #24905561 | C2 | semidirect |
| 15. #19127505 | C4 | semidirect |
| 16. #19127502 | C4 | semidirect |
| 156. C83 | #13153 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909175 | 2 |
| C2×#19127478 | 2 |
| #24908357 | 2 |
| #24908199 | 2 |
| #24905572 | 2 |
| #24905561 | 2 |
| C2×#360×C83 | 2 |
| #13153 | 83 |