Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
432 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 93 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. #26022040 | C2 | semidirect |
| 3. #26021964 | C2 | semidirect |
| 4. C2×#19151379 | C2 | semidirect |
| 5. #26020282 | C2 | semidirect |
| 6. #26018359 | C2 | semidirect |
| 7. C2×#360×C89 | C2 | semidirect |
| 72. M32×C89 | D4 | semidirect |
| 210. C2×#360 | D89 | semidirect |
| 215. C89 | #13386 | semidirect |
| 269. M32 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029857 | 2 |
| #26022040 | 2 |
| #26021964 | 2 |
| C2×#19151379 | 2 |
| #26020282 | 2 |
| #26018359 | 2 |
| C2×#360×C89 | 2 |
| #13386 | 89 |