Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
556 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 4. #24906144 | C2 | semidirect |
| 5. #24905918 | C2 | semidirect |
| 6. #24905301 | C2 | semidirect |
| 7. C83×#3165 | C2 | semidirect |
| 97. M16×C83 | SD16 | semidirect |
| 174. #3165 | D83 | semidirect |
| 180. C83 | #10161 | semidirect |
| 266. M16 | #13050577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918401 | 2 |
| C2×#19128049 | 2 |
| #24908303 | 2 |
| #24906144 | 2 |
| #24905918 | 2 |
| #24905301 | 2 |
| C83×#3165 | 2 |
| #10161 | 83 |