Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
452 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 95 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. #24916633 | C2 | semidirect |
| 3. #24908295 | C2 | semidirect |
| 4. #24905933 | C2 | semidirect |
| 5. #24905356 | C2 | semidirect |
| 6. #24905354 | C2 | semidirect |
| 7. C83×#1500 | C2 | semidirect |
| 9. #19128111 | C4 | semidirect |
| 10. #19128091 | C4 | semidirect |
| 11. #19128067 | C4 | semidirect |
| 12. #19128060 | C4 | semidirect |
| 219. #1500 | D83 | semidirect |
| 223. C83 | #8997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918059 | 2 |
| #24916633 | 2 |
| #24908295 | 2 |
| #24905933 | 2 |
| #24905356 | 2 |
| #24905354 | 2 |
| C83×#1500 | 2 |
| #8997 | 83 |