Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
322 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 322 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 |
|---|---|---|
| 3. #24905637 | C2 | semidirect |
| 5. C2×#14581784 | C4 | semidirect |
| 8. #19128055 | C4 | semidirect |
| 13. C4×#13050574 | C4 | semidirect |
| 136. C83 | #13604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917863 | 2 |
| #24909148 | 2 |
| #24905637 | 2 |
| C83×#2126 | 2 |
| #13604 | 83 |