Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
286 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 65 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. #24909746 | C2 | semidirect |
| 4. #24905516 | C2 | semidirect |
| 5. #24905445 | C2 | semidirect |
| 7. C83×#1694 | C2 | semidirect |
| 66. D664 | Q16 | semidirect |
| 139. #1694 | D83 | semidirect |
| 143. C83 | #12414 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24920423 | 2 |
| #24909746 | 2 |
| #24909607 | 2 |
| #24905516 | 2 |
| #24905445 | 2 |
| #24905429 | 2 |
| C83×#1694 | 2 |
| #12414 | 83 |