Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
386 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 386 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. #24909210 | C2 | semidirect |
| 3. C2×#19127509 | C2 | semidirect |
| 4. C2×#19127484 | C2 | semidirect |
| 5. #24907510 | C2 | semidirect |
| 6. #24905566 | C2 | semidirect |
| 7. C2×#368×C83 | C2 | semidirect |
| 176. C2×#368 | D83 | semidirect |
| 182. C83 | #13392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917184 | 2 |
| #24909210 | 2 |
| C2×#19127509 | 2 |
| C2×#19127484 | 2 |
| #24907510 | 2 |
| #24905566 | 2 |
| C2×#368×C83 | 2 |
| #13392 | 83 |