Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
540 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 540 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. C2×#19127513 | C2 | semidirect |
| 3. #24909178 | C2 | semidirect |
| 4. #24905545 | C2 | semidirect |
| 5. C83×#1945 | C2 | semidirect |
| 40. #107×C83 | D4 | semidirect |
| 122. #1945 | D83 | semidirect |
| 124. C83 | #13413 | semidirect |
| 159. #107 | D332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128078 | 2 |
| C2×#19127513 | 2 |
| #24909178 | 2 |
| #24905545 | 2 |
| C83×#1945 | 2 |
| #13413 | 83 |