Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
454 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 2. #24918012 | C2 | semidirect |
| 3. #24905935 | C2 | semidirect |
| 5. #24905819 | C2 | semidirect |
| 6. #24905334 | C2 | semidirect |
| 189. C83 | #10126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918474 | 2 |
| #24918012 | 2 |
| #24905935 | 2 |
| #24905880 | 2 |
| #24905819 | 2 |
| #24905334 | 2 |
| C83×#3234 | 2 |
| #10126 | 83 |