Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
330 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 107 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. C2×#19151432 | C2 | semidirect |
| 3. #26018429 | C2 | semidirect |
| 4. C89×#2158 | C2 | semidirect |
| 8. C2×D1424 | C4 | semidirect |
| 11. C2×#15667918 | C22 | semidirect |
| 15. #366×C89 | C22 | semidirect |
| 84. #2158 | D89 | semidirect |
| 86. C89 | #13617 | semidirect |
| 97. #366 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1424 | 2 |
| C2×#19151432 | 2 |
| #26018429 | 2 |
| C89×#2158 | 2 |
| #13617 | 89 |