Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
412 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 103 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. #24905474 | C2 | semidirect |
| 5. C22×Dic332 | C4 | semidirect |
| 10. #19127942 | C4 | semidirect |
| 12. C2×#14581726 | C4 | semidirect |
| 150. C83 | #11889 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19127942 | 2 |
| #24909074 | 2 |
| #24905474 | 2 |
| C83×#1807 | 2 |
| #11889 | 83 |