Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1194 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 1194 conjugacy classes of subgroups — too many to draw. Only its 235 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. #26028887 | C2 | semidirect |
| 3. #26021098 | C2 | semidirect |
| 4. #26021094 | C2 | semidirect |
| 6. #26020175 | C2 | semidirect |
| 177. C89 | #21802 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152169 | 2 |
| #26028887 | 2 |
| #26021098 | 2 |
| #26021094 | 2 |
| #26020180 | 2 |
| #26020175 | 2 |
| C89×#1785 | 2 |
| #21802 | 89 |