Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
478 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 478 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. #24906101 | C2 | semidirect |
| 5. #24905807 | C2 | semidirect |
| 6. #24905325 | C2 | semidirect |
| 7. C83×#3104 | C2 | semidirect |
| 191. #3104 | D83 | semidirect |
| 196. C83 | #10041 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918470 | 2 |
| #24917585 | 2 |
| #24906101 | 2 |
| #24905933 | 2 |
| #24905807 | 2 |
| #24905325 | 2 |
| C83×#3104 | 2 |
| #10041 | 83 |