Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
560 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 107 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. #24918604 | C2 | semidirect |
| 4. #24908415 | C2 | semidirect |
| 6. #24905314 | C2 | semidirect |
| 7. C83×#1986 | C2 | semidirect |
| 111. M16×C83 | SD16 | semidirect |
| 197. #1986 | D83 | semidirect |
| 200. C83 | #10206 | semidirect |
| 293. M16 | #13050577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918775 | 2 |
| #24918604 | 2 |
| #24917922 | 2 |
| #24908415 | 2 |
| #24905957 | 2 |
| #24905314 | 2 |
| C83×#1986 | 2 |
| #10206 | 83 |