Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
380 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 105 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. C2×#19127530 | C2 | semidirect |
| 5. #24905576 | C2 | semidirect |
| 6. #24905552 | C2 | semidirect |
| 7. C83×#1953 | C2 | semidirect |
| 18. #19127507 | C4 | semidirect |
| 145. #1953 | D83 | semidirect |
| 148. C83 | #12947 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916381 | 2 |
| C2×#19127530 | 2 |
| #24909190 | 2 |
| C2×#19127507 | 2 |
| #24905576 | 2 |
| #24905552 | 2 |
| C83×#1953 | 2 |
| #12947 | 83 |