Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
300 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 65 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. #24906864 | C2 | semidirect |
| 5. #24905441 | C2 | semidirect |
| 6. #24905427 | C2 | semidirect |
| 7. C83×#2227 | C2 | semidirect |
| 129. #2227 | D83 | semidirect |
| 134. C83 | #12385 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24920473 | 2 |
| #24909688 | 2 |
| #24906864 | 2 |
| #24905510 | 2 |
| #24905441 | 2 |
| #24905427 | 2 |
| C83×#2227 | 2 |
| #12385 | 83 |