Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
554 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 125 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. #24908291 | C2 | semidirect |
| 3. C42×C83⋊C8 | C2 | semidirect |
| 4. #24906221 | C2 | semidirect |
| 5. #24905914 | C2 | semidirect |
| 6. #24905913 | C2 | semidirect |
| 7. C83×#1962 | C2 | semidirect |
| 9. #19128104 | C4 | semidirect |
| 10. #19128077 | C4 | semidirect |
| 11. #19128049 | C4 | semidirect |
| 12. #19128047 | C4 | semidirect |
| 108. C42×C83 | D8 | semidirect |
| 149. C83⋊C8 | #104 | semidirect |
| 179. #1962 | D83 | semidirect |
| 184. C83 | #9844 | semidirect |
| 285. C42 | #13050575 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918038 | 2 |
| #24908291 | 2 |
| C42×C83⋊C8 | 2 |
| #24906221 | 2 |
| #24905914 | 2 |
| #24905913 | 2 |
| C83×#1962 | 2 |
| #9844 | 83 |