Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
318 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
| 3. #24908904 | C2 | semidirect |
| 4. #24905482 | C2 | semidirect |
| 5. #24905478 | C2 | semidirect |
| 6. #24905388 | C2 | semidirect |
| 7. C83×#2232 | C2 | semidirect |
| 159. #2232 | D83 | semidirect |
| 164. C83 | #12287 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918359 | 2 |
| #24909665 | 2 |
| #24908904 | 2 |
| #24905482 | 2 |
| #24905478 | 2 |
| #24905388 | 2 |
| C83×#2232 | 2 |
| #12287 | 83 |