Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
602 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 99 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×#19151392 | C2 | semidirect |
| 4. C4×#15667927 | C2 | semidirect |
| 5. C89×#1799 | C2 | semidirect |
| 7. C2×#15668000 | C4 | semidirect |
| 12. #19151503 | C4 | semidirect |
| 13. #19151499 | C4 | semidirect |
| 16. C4×C4⋊Dic89 | C4 | semidirect |
| 229. #1799 | D89 | semidirect |
| 231. C89 | #13225 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025219 | 2 |
| C2×#19151392 | 2 |
| C2×#19151390 | 2 |
| C4×#15667927 | 2 |
| C89×#1799 | 2 |
| #13225 | 89 |