Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
494 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 109 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. #24906135 | C2 | semidirect |
| 5. #24905321 | C2 | semidirect |
| 6. #24905294 | C2 | semidirect |
| 7. C83×#1960 | C2 | semidirect |
| 10. #19128104 | C4 | semidirect |
| 11. #19128049 | C4 | semidirect |
| 184. #1960 | D83 | semidirect |
| 189. C83 | #9291 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918584 | 2 |
| #24916182 | 2 |
| #24906135 | 2 |
| #24906022 | 2 |
| #24905321 | 2 |
| #24905294 | 2 |
| C83×#1960 | 2 |
| #9291 | 83 |