Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
414 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 414 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 |
|---|---|---|
| 3. #24908444 | C2 | semidirect |
| 5. #24905935 | C2 | semidirect |
| 6. #24905353 | C2 | semidirect |
| 7. C83×#1300 | C2 | semidirect |
| 10. #19128110 | C4 | semidirect |
| 11. #19128095 | C4 | semidirect |
| 12. #19128070 | C4 | semidirect |
| 13. #19128061 | C4 | semidirect |
| 204. #1300 | D83 | semidirect |
| 206. C83 | #8998 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918069 | 2 |
| #24916635 | 2 |
| #24908444 | 2 |
| #24905947 | 2 |
| #24905935 | 2 |
| #24905353 | 2 |
| C83×#1300 | 2 |
| #8998 | 83 |