Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
508 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 103 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. #24910644 | C2 | semidirect |
| 2. #24906189 | C2 | semidirect |
| 4. #24905328 | C2 | semidirect |
| 16. #494×C83 | C4 | semidirect |
| 17. #492×C83 | C4 | semidirect |
| 122. C83 | #9429 | semidirect |
| 127. #494 | Dic83 | semidirect |
| 128. #492 | Dic83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24910644 | 2 |
| #24906189 | 2 |
| #24906010 | 2 |
| #24905328 | 2 |
| C83×#3152 | 2 |
| #9429 | 83 |