Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
456 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 456 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. #24910568 | C2 | semidirect |
| 3. #24906089 | C2 | semidirect |
| 6. #24905357 | C2 | semidirect |
| 7. C83×#1300 | C2 | semidirect |
| 10. #19128070 | C4 | semidirect |
| 11. #19128066 | C4 | semidirect |
| 196. #1300 | D83 | semidirect |
| 197. C83 | #9442 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917864 | 2 |
| #24910568 | 2 |
| #24906089 | 2 |
| #24905972 | 2 |
| #24905970 | 2 |
| #24905357 | 2 |
| C83×#1300 | 2 |
| #9442 | 83 |