Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
496 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 83 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. #24913584 | C2 | semidirect |
| 4. #24906181 | C2 | semidirect |
| 6. #24905357 | C2 | semidirect |
| 7. C83×#1528 | C2 | semidirect |
| 178. #1528 | D83 | semidirect |
| 181. C83 | #10093 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918653 | 2 |
| #24917857 | 2 |
| #24913584 | 2 |
| #24906181 | 2 |
| #24905972 | 2 |
| #24905357 | 2 |
| C83×#1528 | 2 |
| #10093 | 83 |