Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
510 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 99 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. #24907499 | C2 | semidirect |
| 3. #24907241 | C2 | semidirect |
| 4. #24905982 | C2 | semidirect |
| 5. #24905828 | C2 | semidirect |
| 8. C22×#13050578 | C4 | semidirect |
| 16. C2×#14581723 | C4 | semidirect |
| 17. C2×#14581715 | C4 | semidirect |
| 18. C2×#14581713 | C4 | semidirect |
| 223. C83 | #9816 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19127928 | 2 |
| #24907499 | 2 |
| #24907241 | 2 |
| #24905982 | 2 |
| #24905828 | 2 |
| #24905823 | 2 |
| C83×#1507 | 2 |
| #9816 | 83 |