Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
396 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 93 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. #24907216 | C2 | semidirect |
| 3. #24906224 | C2 | semidirect |
| 5. #24905975 | C2 | semidirect |
| 7. C83×#1531 | C2 | semidirect |
| 9. #19128097 | C4 | semidirect |
| 10. #19128075 | C4 | semidirect |
| 11. #19128051 | C4 | semidirect |
| 12. #19128049 | C4 | semidirect |
| 180. #1531 | D83 | semidirect |
| 184. C83 | #9766 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918023 | 2 |
| #24907216 | 2 |
| #24906224 | 2 |
| #24906073 | 2 |
| #24905975 | 2 |
| #24905972 | 2 |
| C83×#1531 | 2 |
| #9766 | 83 |