Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
370 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 73 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. #24907603 | C2 | semidirect |
| 3. #24906183 | C2 | semidirect |
| 4. #24906075 | C2 | semidirect |
| 5. #24906074 | C2 | semidirect |
| 6. #24905373 | C2 | semidirect |
| 7. C83×#1557 | C2 | semidirect |
| 165. #1557 | D83 | semidirect |
| 169. C83 | #10525 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918841 | 2 |
| #24907603 | 2 |
| #24906183 | 2 |
| #24906075 | 2 |
| #24906074 | 2 |
| #24905373 | 2 |
| C83×#1557 | 2 |
| #10525 | 83 |