Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
424 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 81 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. #24906254 | C2 | semidirect |
| 5. #24905884 | C2 | semidirect |
| 6. #24905352 | C2 | semidirect |
| 7. C83×#1561 | C2 | semidirect |
| 168. #1561 | D83 | semidirect |
| 172. C83 | #10492 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918401 | 2 |
| #24908302 | 2 |
| #24906254 | 2 |
| #24906132 | 2 |
| #24905884 | 2 |
| #24905352 | 2 |
| C83×#1561 | 2 |
| #10492 | 83 |