Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
458 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 113 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. #24905571 | C2 | semidirect |
| 6. #24905557 | C2 | semidirect |
| 7. C2×#358×C83 | C2 | semidirect |
| 16. #19127973 | C4 | semidirect |
| 174. C2×#358 | D83 | semidirect |
| 178. C83 | #13072 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128117 | 2 |
| C2×#19127973 | 2 |
| C2×#19127517 | 2 |
| #24907528 | 2 |
| #24905571 | 2 |
| #24905557 | 2 |
| C2×#358×C83 | 2 |
| #13072 | 83 |