Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
442 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 85 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. #24916533 | C2 | semidirect |
| 3. #24906011 | C2 | semidirect |
| 4. #24906010 | C2 | semidirect |
| 5. #24905334 | C2 | semidirect |
| 6. #24905329 | C2 | semidirect |
| 7. C83×#1536 | C2 | semidirect |
| 9. #19128097 | C4 | semidirect |
| 10. #19128077 | C4 | semidirect |
| 11. #19128049 | C4 | semidirect |
| 12. #19128047 | C4 | semidirect |
| 170. #1536 | D83 | semidirect |
| 175. C83 | #9417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918197 | 2 |
| #24916533 | 2 |
| #24906011 | 2 |
| #24906010 | 2 |
| #24905334 | 2 |
| #24905329 | 2 |
| C83×#1536 | 2 |
| #9417 | 83 |