Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
372 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 83 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. #26021871 | C2 | semidirect |
| 3. #26018203 | C2 | semidirect |
| 4. #26018189 | C2 | semidirect |
| 5. C89×#1327 | C2 | semidirect |
| 140. #1327 | D89 | semidirect |
| 142. C89 | #11485 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028963 | 2 |
| #26021871 | 2 |
| #26018203 | 2 |
| #26018189 | 2 |
| C89×#1327 | 2 |
| #11485 | 89 |