Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
356 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 89 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. #24907603 | C2 | semidirect |
| 3. #24906233 | C2 | semidirect |
| 6. #24905293 | C2 | semidirect |
| 7. C83×#1571 | C2 | semidirect |
| 136. #1571 | D83 | semidirect |
| 141. C83 | #10659 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24908260 | 2 |
| #24907603 | 2 |
| #24906233 | 2 |
| #24905889 | 2 |
| #24905887 | 2 |
| #24905293 | 2 |
| C83×#1571 | 2 |
| #10659 | 83 |