Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
942 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 942 conjugacy classes of subgroups — too many to draw. Only its 155 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 |
|---|---|---|
| 1. #24921863 | C2 | semidirect |
| 2. #24918454 | C2 | semidirect |
| 3. #24906784 | C2 | semidirect |
| 4. #24906755 | C2 | semidirect |
| 5. #24906101 | C2 | semidirect |
| 6. #24906073 | C2 | semidirect |
| 7. C83×#3135 | C2 | semidirect |
| 165. #3135 | D83 | semidirect |
| 170. C83 | #19061 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24921863 | 2 |
| #24918454 | 2 |
| #24906784 | 2 |
| #24906755 | 2 |
| #24906101 | 2 |
| #24906073 | 2 |
| C83×#3135 | 2 |
| #19061 | 83 |