Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
498 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 498 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 |
|---|---|---|
| 2. #24916602 | C2 | semidirect |
| 3. #24908390 | C2 | semidirect |
| 4. #24906176 | C2 | semidirect |
| 5. #24905332 | C2 | semidirect |
| 6. #24905319 | C2 | semidirect |
| 7. C83×#1509 | C2 | semidirect |
| 9. #19128091 | C4 | semidirect |
| 10. #19128067 | C4 | semidirect |
| 220. #1509 | D83 | semidirect |
| 223. C83 | #9378 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918478 | 2 |
| #24916602 | 2 |
| #24908390 | 2 |
| #24906176 | 2 |
| #24905332 | 2 |
| #24905319 | 2 |
| C83×#1509 | 2 |
| #9378 | 83 |