Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
440 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 99 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. #24908452 | C2 | semidirect |
| 3. #24908386 | C2 | semidirect |
| 4. #24906215 | C2 | semidirect |
| 6. #24905366 | C2 | semidirect |
| 104. M16×C83 | SD16 | semidirect |
| 194. C83 | #10501 | semidirect |
| 282. M16 | #13050578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918385 | 2 |
| #24908452 | 2 |
| #24908386 | 2 |
| #24906215 | 2 |
| #24906140 | 2 |
| #24905366 | 2 |
| C83×#1980 | 2 |
| #10501 | 83 |