Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
424 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 3. #24908016 | C2 | semidirect |
| 5. #24907751 | C2 | semidirect |
| 6. #24905591 | C2 | semidirect |
| 7. C83×#2129 | C2 | semidirect |
| 196. #2129 | D83 | semidirect |
| 202. C83 | #13433 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918330 | 2 |
| #24909112 | 2 |
| #24908016 | 2 |
| #24907988 | 2 |
| #24907751 | 2 |
| #24905591 | 2 |
| C83×#2129 | 2 |
| #13433 | 83 |