Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
738 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 155 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. #24908411 | C2 | semidirect |
| 4. #24905304 | C2 | semidirect |
| 9. #19128073 | C4 | semidirect |
| 28. #14581792 | C2×C4 | semidirect |
| 33. C4×C83⋊C8 | C2×C4 | semidirect |
| 83. C4⋊C4×C83 | SD16 | semidirect |
| 158. C83 | #9064 | semidirect |
| 236. C4⋊C4 | #13050578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128073 | 2 |
| #24908411 | 2 |
| C2×#19127445 | 2 |
| #24905304 | 2 |
| C83×#2366 | 2 |
| #9064 | 83 |