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 |
|---|---|---|
| 3. C2×#19127517 | C2 | semidirect |
| 5. #24908251 | C2 | semidirect |
| 6. #24905550 | C2 | semidirect |
| 7. C2×#362×C83 | C2 | semidirect |
| 172. C2×#362 | D83 | semidirect |
| 176. C83 | #13418 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917952 | 2 |
| #24909210 | 2 |
| C2×#19127517 | 2 |
| #24909192 | 2 |
| #24908251 | 2 |
| #24905550 | 2 |
| C2×#362×C83 | 2 |
| #13418 | 83 |