Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
498 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 119 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. #24908381 | C2 | semidirect |
| 3. #24905957 | C2 | semidirect |
| 4. #24905752 | C2 | semidirect |
| 5. C4×#106×C83 | C2 | semidirect |
| 7. #19128106 | C4 | semidirect |
| 8. #19128078 | C4 | semidirect |
| 9. #19128048 | C4 | semidirect |
| 117. C8×C83 | #104 | semidirect |
| 144. C4×#106 | D83 | semidirect |
| 147. C83 | #9721 | semidirect |
| 261. C8 | #14581720 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918042 | 2 |
| #24908381 | 2 |
| #24905957 | 2 |
| #24905752 | 2 |
| C4×#106×C83 | 2 |
| #9721 | 83 |