Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
544 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 105 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. #24908308 | C2 | semidirect |
| 5. #24905918 | C2 | semidirect |
| 6. #24905299 | C2 | semidirect |
| 7. C83×#3229 | C2 | semidirect |
| 174. #3229 | D83 | semidirect |
| 181. C83 | #10151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917839 | 2 |
| C2×#19128049 | 2 |
| #24908308 | 2 |
| #24906130 | 2 |
| #24905918 | 2 |
| #24905299 | 2 |
| C83×#3229 | 2 |
| #10151 | 83 |