Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
490 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 85 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. #24917594 | C2 | semidirect |
| 4. #24908402 | C2 | semidirect |
| 5. #24906079 | C2 | semidirect |
| 7. C83×#1290 | C2 | semidirect |
| 200. #1290 | D83 | semidirect |
| 201. C83 | #10029 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918780 | 2 |
| #24917594 | 2 |
| #24917586 | 2 |
| #24908402 | 2 |
| #24906079 | 2 |
| #24906075 | 2 |
| C83×#1290 | 2 |
| #10029 | 83 |