Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
592 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 101 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. #24918775 | C2 | semidirect |
| 3. #24908391 | C2 | semidirect |
| 4. #24908382 | C2 | semidirect |
| 5. #24905962 | C2 | semidirect |
| 6. #24905314 | C2 | semidirect |
| 7. C83×#3138 | C2 | semidirect |
| 209. #3138 | D83 | semidirect |
| 214. C83 | #10193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918775 | 2 |
| #24918381 | 2 |
| #24908391 | 2 |
| #24908382 | 2 |
| #24905962 | 2 |
| #24905314 | 2 |
| C83×#3138 | 2 |
| #10193 | 83 |