Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
422 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 89 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. C2×#19127513 | C2 | semidirect |
| 3. #24909180 | C2 | semidirect |
| 4. #24909090 | C2 | semidirect |
| 5. #24907518 | C2 | semidirect |
| 6. #24905564 | C2 | semidirect |
| 7. C83×#2155 | C2 | semidirect |
| 57. C2×C16×C83 | D4 | semidirect |
| 167. #2155 | D83 | semidirect |
| 173. C83 | #13396 | semidirect |
| 219. C2×C16 | D332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917112 | 2 |
| C2×#19127513 | 2 |
| #24909180 | 2 |
| #24909090 | 2 |
| #24907518 | 2 |
| #24905564 | 2 |
| C83×#2155 | 2 |
| #13396 | 83 |