Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1190 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1190 conjugacy classes of subgroups — too many to draw. Only its 171 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×#19151400 | C2 | semidirect |
| 3. #26020281 | C2 | semidirect |
| 4. C2×C22⋊C16×C89 | C2 | semidirect |
| 9. C22×D712 | C4 | semidirect |
| 11. C2×#15667946 | C22 | semidirect |
| 16. C22×C16×C89 | C22 | semidirect |
| 64. D712 | C22⋊C4 | semidirect |
| 122. C22×C89 | #357 | semidirect |
| 149. C2×C22⋊C16 | D89 | semidirect |
| 151. C89 | #12731 | semidirect |
| 159. C22×C16 | C2×D89 | semidirect |
| 275. C22 | #19151400 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D712 | 2 |
| C2×#19151400 | 2 |
| #26020281 | 2 |
| C2×C22⋊C16×C89 | 2 |
| #12731 | 89 |