Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
470 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 93 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. #24916123 | C2 | semidirect |
| 3. #24907559 | C2 | semidirect |
| 5. #24905370 | C2 | semidirect |
| 6. #24905351 | C2 | semidirect |
| 16. #19127741 | C4 | semidirect |
| 17. #19127741 | C4 | semidirect |
| 19. #19127706 | C4 | semidirect |
| 20. #19127706 | C4 | semidirect |
| 230. C83 | #9348 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917399 | 2 |
| #24916123 | 2 |
| #24907559 | 2 |
| #24906031 | 2 |
| #24905370 | 2 |
| #24905351 | 2 |
| C83×#1471 | 2 |
| #9348 | 83 |