Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
334 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 334 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. #19128258 | C4 | semidirect |
| 8. #19128055 | C4 | semidirect |
| 13. C4×#13050574 | C4 | semidirect |
| 23. #14581784 | C2×C4 | semidirect |
| 34. C4×C83⋊C8 | C2×C4 | semidirect |
| 141. C83 | #13603 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917849 | 2 |
| C2×#19127498 | 2 |
| #24905637 | 2 |
| C2×#354×C83 | 2 |
| #13603 | 83 |