Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
506 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 506 conjugacy classes of subgroups — too many to draw. Only its 83 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. #24918388 | C2 | semidirect |
| 3. C2×#19128063 | C2 | semidirect |
| 4. #24906075 | C2 | semidirect |
| 5. #24905816 | C2 | semidirect |
| 6. #24905361 | C2 | semidirect |
| 7. C83×#1556 | C2 | semidirect |
| 187. #1556 | D83 | semidirect |
| 191. C83 | #10136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918452 | 2 |
| #24918388 | 2 |
| C2×#19128063 | 2 |
| #24906075 | 2 |
| #24905816 | 2 |
| #24905361 | 2 |
| C83×#1556 | 2 |
| #10136 | 83 |