Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
444 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 107 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. #24905452 | C2 | direct (N × H) |
| 5. C22×Dic332 | C4 | semidirect |
| 10. #19127959 | C4 | semidirect |
| 12. C2×#14581724 | C4 | semidirect |
| 24. C2×Dic332 | C2×C4 | semidirect |
| 40. #14581724 | C2×C4 | semidirect |
| 165. C2×C83 | #1340 | semidirect |
| 171. C83 | C2×#1340 | semidirect |
| 331. C2 | #24905452 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19127959 | 2 |
| C2×#19127458 | 2 |
| #24905452 | 2 |
| C2×#349×C83 | 2 |
| C2×#1340 | 83 |