Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
380 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 3. #24906230 | C2 | semidirect |
| 4. #24906193 | C2 | semidirect |
| 6. #24905335 | C2 | semidirect |
| 7. C83×#1526 | C2 | semidirect |
| 186. #1526 | D83 | semidirect |
| 188. C83 | #10498 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918462 | 2 |
| #24908312 | 2 |
| #24906230 | 2 |
| #24906193 | 2 |
| #24906060 | 2 |
| #24905335 | 2 |
| C83×#1526 | 2 |
| #10498 | 83 |