Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
590 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 151 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 |
|---|---|---|
| 1. #24917976 | C2 | semidirect |
| 3. #24909708 | C2 | semidirect |
| 4. #24909706 | C2 | semidirect |
| 5. #24909705 | C2 | semidirect |
| 6. #24909701 | C2 | semidirect |
| 7. #24909169 | C2 | semidirect |
| 8. #346×D83 | C2 | semidirect |
| 9. C83×#2245 | C2 | semidirect |
| 152. #2245 | D83 | semidirect |
| 158. C83 | #33701 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917976 | 2 |
| #24917892 | 2 |
| #24909708 | 2 |
| #24909706 | 2 |
| #24909705 | 2 |
| #24909701 | 2 |
| #24909169 | 2 |
| #346×D83 | 2 |
| C83×#2245 | 2 |
| #33701 | 83 |