Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
494 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 109 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. #24908283 | C2 | semidirect |
| 4. #24906134 | C2 | semidirect |
| 6. #24905322 | C2 | semidirect |
| 7. C83×#1275 | C2 | semidirect |
| 11. #19128106 | C4 | semidirect |
| 12. #19128048 | C4 | semidirect |
| 188. #1275 | D83 | semidirect |
| 189. C83 | #9291 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918586 | 2 |
| #24916182 | 2 |
| #24908283 | 2 |
| #24906134 | 2 |
| #24906024 | 2 |
| #24905322 | 2 |
| C83×#1275 | 2 |
| #9291 | 83 |