Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
450 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 107 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. C4×#14581731 | C2 | semidirect |
| 3. #24906210 | C2 | semidirect |
| 4. #24905425 | C2 | semidirect |
| 5. #24905424 | C2 | semidirect |
| 6. #24905423 | C2 | semidirect |
| 7. C83×#1331 | C2 | semidirect |
| 21. C4×C83⋊C16 | C22 | semidirect |
| 22. #19127454 | C22 | semidirect |
| 25. C4×C16×C83 | C22 | semidirect |
| 26. #335×C83 | C22 | semidirect |
| 32. D8×D83 | C8 | semidirect |
| 178. #1331 | D83 | semidirect |
| 179. C83 | #11593 | semidirect |
| 195. C4×C16 | C2×D83 | semidirect |
| 197. #335 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D8×D83 | 2 |
| C4×#14581731 | 2 |
| #24906210 | 2 |
| #24905425 | 2 |
| #24905424 | 2 |
| #24905423 | 2 |
| C83×#1331 | 2 |
| #11593 | 83 |