Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
454 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 95 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. #24909210 | C2 | semidirect |
| 3. C2×#19127513 | C2 | semidirect |
| 4. C2×#19127513 | C2 | semidirect |
| 5. #24909190 | C2 | semidirect |
| 6. #24905549 | C2 | semidirect |
| 7. C83×#1953 | C2 | semidirect |
| 65. #108×C83 | D4 | semidirect |
| 180. #1953 | D83 | semidirect |
| 182. C83 | #13417 | semidirect |
| 240. #108 | D332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917949 | 2 |
| #24909210 | 2 |
| C2×#19127513 | 2 |
| #24909190 | 2 |
| #24905549 | 2 |
| C83×#1953 | 2 |
| #13417 | 83 |