Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
328 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 97 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. C2×#19151376 | C2 | semidirect |
| 4. #26020990 | C2 | semidirect |
| 5. #26018362 | C2 | semidirect |
| 6. #26018352 | C2 | semidirect |
| 14. #19151402 | C4 | semidirect |
| 15. #19151399 | C4 | semidirect |
| 156. C89 | #13153 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151408 | 2 |
| #26021964 | 2 |
| C2×#19151376 | 2 |
| #26020990 | 2 |
| #26018362 | 2 |
| #26018352 | 2 |
| C89×#1975 | 2 |
| #13153 | 89 |