Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
428 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 123 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. #26020424 | C2 | semidirect |
| 3. #26018708 | C2 | semidirect |
| 4. #26018708 | C2 | semidirect |
| 7. C2×#322×C89 | C2 | semidirect |
| 165. C2×#322 | D89 | semidirect |
| 166. C89 | #9858 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030575 | 2 |
| #26020424 | 2 |
| #26018708 | 2 |
| #26018704 | 2 |
| C2×#322×C89 | 2 |
| #9858 | 89 |