Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
316 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 63 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. #24909665 | C2 | semidirect |
| 4. #24905474 | C2 | semidirect |
| 6. #24905403 | C2 | semidirect |
| 7. C83×#2087 | C2 | semidirect |
| 156. #2087 | D83 | semidirect |
| 160. C83 | #12293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918815 | 2 |
| #24909665 | 2 |
| #24909648 | 2 |
| #24905474 | 2 |
| #24905471 | 2 |
| #24905403 | 2 |
| C83×#2087 | 2 |
| #12293 | 83 |