Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
374 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 374 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. #26021025 | C2 | semidirect |
| 3. #26019024 | C2 | semidirect |
| 4. #26019002 | C2 | semidirect |
| 7. C89×#1292 | C2 | semidirect |
| 164. #1292 | D89 | semidirect |
| 165. C89 | #10607 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021091 | 2 |
| #26021025 | 2 |
| #26019024 | 2 |
| #26019002 | 2 |
| #26018921 | 2 |
| C2×#19151341 | 2 |
| C89×#1292 | 2 |
| #10607 | 89 |