Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
954 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 954 conjugacy classes of subgroups — too many to draw. Only its 163 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 |
|---|---|---|
| 1. #24921877 | C2 | semidirect |
| 2. #24918850 | C2 | semidirect |
| 3. #24906601 | C2 | semidirect |
| 4. #24906582 | C2 | semidirect |
| 5. #24906539 | C2 | semidirect |
| 6. #24906520 | C2 | semidirect |
| 7. #24906198 | C2 | semidirect |
| 8. #24905919 | C2 | semidirect |
| 200. C83 | #18688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24921877 | 2 |
| #24918850 | 2 |
| #24906601 | 2 |
| #24906582 | 2 |
| #24906539 | 2 |
| #24906520 | 2 |
| #24906198 | 2 |
| #24905919 | 2 |
| C83×#3147 | 2 |
| #18688 | 83 |