Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
290 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 59 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. #24905480 | C2 | semidirect |
| 6. #24905405 | C2 | semidirect |
| 7. C83×#2089 | C2 | semidirect |
| 146. #2089 | D83 | semidirect |
| 150. C83 | #12297 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918924 | 2 |
| #24909665 | 2 |
| #24909643 | 2 |
| #24905480 | 2 |
| #24905477 | 2 |
| #24905405 | 2 |
| C83×#2089 | 2 |
| #12297 | 83 |