Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
800 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 115 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. #24908439 | C2 | semidirect |
| 3. #24908292 | C2 | semidirect |
| 4. #24908290 | C2 | semidirect |
| 5. #24906200 | C2 | semidirect |
| 6. #24906196 | C2 | semidirect |
| 7. C83×#1560 | C2 | semidirect |
| 8. #19128445 | C4 | semidirect |
| 247. #1560 | D83 | semidirect |
| 248. C83 | #8532 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24921861 | 2 |
| #24908439 | 2 |
| #24908292 | 2 |
| #24908290 | 2 |
| #24906200 | 2 |
| #24906196 | 2 |
| C83×#1560 | 2 |
| #8532 | 83 |