Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
338 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 57 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. #24909649 | C2 | semidirect |
| 3. #24909641 | C2 | semidirect |
| 4. #24908905 | C2 | semidirect |
| 5. #24905477 | C2 | semidirect |
| 6. #24905388 | C2 | semidirect |
| 7. C83×#1349 | C2 | semidirect |
| 15. C2×#14581726 | C22 | semidirect |
| 22. C22⋊(C83⋊C16) | C22 | semidirect |
| 25. C22⋊C16×C83 | C22 | semidirect |
| 26. #341×C83 | C22 | semidirect |
| 169. #1349 | D83 | semidirect |
| 171. C83 | #12284 | semidirect |
| 188. C22⋊C16 | C2×D83 | semidirect |
| 190. #341 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918323 | 2 |
| #24909649 | 2 |
| #24909641 | 2 |
| #24908905 | 2 |
| #24905477 | 2 |
| #24905388 | 2 |
| C83×#1349 | 2 |
| #12284 | 83 |