Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
462 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 99 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. #24906065 | C2 | semidirect |
| 5. #24905327 | C2 | semidirect |
| 6. #24905319 | C2 | semidirect |
| 7. C83×#2336 | C2 | semidirect |
| 9. #19128111 | C4 | semidirect |
| 10. #19128067 | C4 | semidirect |
| 199. #2336 | D83 | semidirect |
| 205. C83 | #9382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918653 | 2 |
| #24908381 | 2 |
| #24906065 | 2 |
| #24906009 | 2 |
| #24905327 | 2 |
| #24905319 | 2 |
| C83×#2336 | 2 |
| #9382 | 83 |