Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
766 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 766 conjugacy classes of subgroups — too many to draw. Only its 111 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. #24906161 | C2 | semidirect |
| 3. #24906156 | C2 | semidirect |
| 4. #24906077 | C2 | semidirect |
| 5. #24906073 | C2 | semidirect |
| 6. #24905804 | C2 | semidirect |
| 7. C83×#1955 | C2 | semidirect |
| 224. #1955 | D83 | semidirect |
| 230. C83 | #8458 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24921315 | 2 |
| #24906161 | 2 |
| #24906156 | 2 |
| #24906077 | 2 |
| #24906073 | 2 |
| #24905804 | 2 |
| C83×#1955 | 2 |
| #8458 | 83 |