Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
524 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 524 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 |
|---|---|---|
| 3. #24918005 | C2 | semidirect |
| 5. #24905961 | C2 | semidirect |
| 6. #24905313 | C2 | semidirect |
| 7. C83×#1987 | C2 | semidirect |
| 89. #13050574 | SD16 | semidirect |
| 192. #1987 | D83 | semidirect |
| 196. C83 | #10197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918780 | 2 |
| #24918388 | 2 |
| #24918005 | 2 |
| #24908381 | 2 |
| #24905961 | 2 |
| #24905313 | 2 |
| C83×#1987 | 2 |
| #10197 | 83 |