Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
922 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 922 conjugacy classes of subgroups — too many to draw. Only its 187 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. #24918041 | C2 | semidirect |
| 2. #24917892 | C2 | semidirect |
| 3. #24917890 | C2 | semidirect |
| 4. #24907079 | C2 | semidirect |
| 5. #24907077 | C2 | semidirect |
| 6. #24907069 | C2 | semidirect |
| 7. #24907054 | C2 | semidirect |
| 8. C82×D83 | C2 | semidirect |
| 9. C83×#1709 | C2 | semidirect |
| 85. C8×D83 | D8 | semidirect |
| 124. C83⋊C8 | #135 | semidirect |
| 150. #1709 | D83 | semidirect |
| 153. C83 | #19603 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918041 | 2 |
| #24917892 | 2 |
| #24917890 | 2 |
| #24907079 | 2 |
| #24907077 | 2 |
| #24907069 | 2 |
| #24907054 | 2 |
| C82×D83 | 2 |
| C83×#1709 | 2 |
| #19603 | 83 |