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. #24906191 | C2 | semidirect |
| 5. #24906057 | C2 | semidirect |
| 6. #24905334 | C2 | semidirect |
| 7. C83×#1569 | C2 | semidirect |
| 183. #1569 | 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 |
|---|---|
| #24918468 | 2 |
| #24908310 | 2 |
| #24906191 | 2 |
| #24906060 | 2 |
| #24906057 | 2 |
| #24905334 | 2 |
| C83×#1569 | 2 |
| #10498 | 83 |