Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
440 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 75 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. #24918679 | C2 | semidirect |
| 4. #24906013 | C2 | semidirect |
| 5. #24906013 | C2 | semidirect |
| 6. C83⋊#1308 | C2 | semidirect |
| 191. C83 | #10210 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918679 | 2 |
| #24918657 | 2 |
| #24918474 | 2 |
| #24906013 | 2 |
| C83⋊#1308 | 2 |
| C83×#1514 | 2 |
| #10210 | 83 |