Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
684 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 3. #26018824 | C2 | semidirect |
| 5. #26018120 | C2 | semidirect |
| 6. #26018119 | C2 | semidirect |
| 7. C89×#1520 | C2 | semidirect |
| 11. #19151533 | C4 | semidirect |
| 13. #19151509 | C4 | semidirect |
| 52. #15667919 | C2×C4 | semidirect |
| 54. C22×Q8×C89 | C2×C4 | semidirect |
| 63. C2×C4⋊C4×C89 | C2×C4 | semidirect |
| 237. #1520 | D89 | semidirect |
| 241. C89 | #9199 | semidirect |
| 262. C22×Q8 | C4×D89 | semidirect |
| 278. C2×C4⋊C4 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26026059 | 2 |
| #26022865 | 2 |
| #26018824 | 2 |
| C2×#19151321 | 2 |
| #26018120 | 2 |
| #26018119 | 2 |
| C89×#1520 | 2 |
| #9199 | 89 |