Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
360 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 1. #24909252 | C2 | semidirect |
| 5. #24905573 | C2 | semidirect |
| 6. #24905545 | C2 | semidirect |
| 7. C83×#1772 | C2 | semidirect |
| 16. #19127513 | C4 | semidirect |
| 154. #1772 | D83 | semidirect |
| 157. C83 | #13136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909252 | 2 |
| C2×#19127513 | 2 |
| #24909178 | 2 |
| #24908329 | 2 |
| #24905573 | 2 |
| #24905545 | 2 |
| C83×#1772 | 2 |
| #13136 | 83 |