Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
420 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 4. #24905866 | C2 | semidirect |
| 5. #24905332 | C2 | semidirect |
| 6. #24905326 | C2 | semidirect |
| 7. C83×#1537 | C2 | semidirect |
| 167. #1537 | D83 | semidirect |
| 171. C83 | #9373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918470 | 2 |
| #24916541 | 2 |
| #24906159 | 2 |
| #24905866 | 2 |
| #24905332 | 2 |
| #24905326 | 2 |
| C83×#1537 | 2 |
| #9373 | 83 |