Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
444 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 89 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. #24910643 | C2 | semidirect |
| 3. #24906181 | C2 | semidirect |
| 6. #24905328 | C2 | semidirect |
| 7. C83×#1288 | C2 | semidirect |
| 11. #19128052 | C4 | semidirect |
| 12. #19128048 | C4 | semidirect |
| 157. #1288 | D83 | semidirect |
| 158. C83 | #9430 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917857 | 2 |
| #24910643 | 2 |
| #24906181 | 2 |
| #24906011 | 2 |
| #24906009 | 2 |
| #24905328 | 2 |
| C83×#1288 | 2 |
| #9430 | 83 |