Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
420 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 85 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. #24906014 | C2 | semidirect |
| 5. #24905334 | C2 | semidirect |
| 6. #24905329 | C2 | semidirect |
| 7. C83×#1537 | C2 | semidirect |
| 9. #19128104 | C4 | semidirect |
| 10. #19128075 | C4 | semidirect |
| 11. #19128051 | C4 | semidirect |
| 12. #19128049 | C4 | semidirect |
| 162. #1537 | D83 | semidirect |
| 167. C83 | #9415 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918182 | 2 |
| #24916533 | 2 |
| #24906014 | 2 |
| #24906011 | 2 |
| #24905334 | 2 |
| #24905329 | 2 |
| C83×#1537 | 2 |
| #9415 | 83 |