Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
286 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 61 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. #24909708 | C2 | semidirect |
| 4. #24905514 | C2 | semidirect |
| 5. #24905433 | C2 | semidirect |
| 7. C83×#2209 | C2 | semidirect |
| 142. #2209 | D83 | semidirect |
| 147. C83 | #12351 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24920039 | 2 |
| #24909708 | 2 |
| #24906949 | 2 |
| #24905514 | 2 |
| #24905433 | 2 |
| #24905420 | 2 |
| C83×#2209 | 2 |
| #12351 | 83 |