Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
930 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26031009 | C2 | semidirect |
| 3. #26023903 | C2 | semidirect |
| 4. #26020182 | C2 | semidirect |
| 5. #26018823 | C2 | semidirect |
| 6. #26018100 | C2 | semidirect |
| 7. C89×#1964 | C2 | semidirect |
| 256. #1964 | D89 | semidirect |
| 260. C89 | #9947 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031009 | 2 |
| C2×#19151731 | 2 |
| #26023903 | 2 |
| #26020182 | 2 |
| #26018823 | 2 |
| #26018100 | 2 |
| C89×#1964 | 2 |
| #9947 | 89 |