Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
284 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 61 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. #24906988 | C2 | semidirect |
| 5. #24905444 | C2 | semidirect |
| 6. #24905433 | C2 | semidirect |
| 7. C83×#2225 | C2 | semidirect |
| 143. #2225 | D83 | semidirect |
| 148. C83 | #12389 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24920540 | 2 |
| #24909702 | 2 |
| #24906988 | 2 |
| #24905507 | 2 |
| #24905444 | 2 |
| #24905433 | 2 |
| C83×#2225 | 2 |
| #12389 | 83 |