Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
378 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 2. #24909228 | C2 | semidirect |
| 4. #24909182 | C2 | semidirect |
| 5. #24908376 | C2 | semidirect |
| 7. C83×#1389 | C2 | semidirect |
| 169. #1389 | D83 | semidirect |
| 170. C83 | #13443 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128144 | 2 |
| #24909228 | 2 |
| #24909210 | 2 |
| #24909182 | 2 |
| #24908376 | 2 |
| #24908359 | 2 |
| C83×#1389 | 2 |
| #13443 | 83 |