Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
1946 conjugacy classes of subgroups; only the 259 normal subgroups are shown.
This group has 1946 conjugacy classes of subgroups — too many to draw. Only its 259 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. #24916092 | C2 | semidirect |
| 3. #24908301 | C2 | semidirect |
| 4. #24907384 | C2 | semidirect |
| 5. #24907383 | C2 | semidirect |
| 6. C83×#1783 | C2 | semidirect |
| 16. #19127724 | C22 | semidirect |
| 17. C2×#14581709 | C22 | semidirect |
| 18. C2×#14581708 | C22 | semidirect |
| 20. M16×Dic83 | C22 | semidirect |
| 22. C2×#100×C83 | C22 | semidirect |
| 137. C2×Dic83 | #100 | semidirect |
| 176. #1783 | D83 | semidirect |
| 177. C83 | #21797 | semidirect |
| 191. C2×#100 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14581788 | 2 |
| #24916092 | 2 |
| #24908301 | 2 |
| #24907384 | 2 |
| #24907383 | 2 |
| C83×#1783 | 2 |
| #21797 | 83 |