Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
1166 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1166 conjugacy classes of subgroups — too many to draw. Only its 251 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 |
|---|---|---|
| 4. #24907458 | C2 | semidirect |
| 6. #24907258 | C2 | semidirect |
| 134. C83 | #20730 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128178 | 2 |
| #24916098 | 2 |
| #24907546 | 2 |
| #24907458 | 2 |
| #24907386 | 2 |
| #24907258 | 2 |
| C83×#1822 | 2 |
| #20730 | 83 |