Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
410 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 83 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. #24909265 | C2 | semidirect |
| 3. #24906217 | C2 | semidirect |
| 4. #24905507 | C2 | semidirect |
| 5. #24905506 | C2 | semidirect |
| 6. #24905505 | C2 | semidirect |
| 7. C83×#1360 | C2 | semidirect |
| 19. C4⋊(C83⋊C16) | C22 | semidirect |
| 22. #19127452 | C22 | semidirect |
| 25. C4⋊C16×C83 | C22 | semidirect |
| 26. #334×C83 | C22 | semidirect |
| 184. #1360 | D83 | semidirect |
| 185. C83 | #11959 | semidirect |
| 199. C4⋊C16 | C2×D83 | semidirect |
| 204. #334 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #495×D83 | 2 |
| #24909265 | 2 |
| #24906217 | 2 |
| #24905507 | 2 |
| #24905506 | 2 |
| #24905505 | 2 |
| C83×#1360 | 2 |
| #11959 | 83 |