Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
434 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 101 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. C4⋊C16×D89 | C2 | semidirect |
| 3. #334×D89 | C2 | semidirect |
| 4. #26018296 | C2 | semidirect |
| 5. #26018295 | C2 | semidirect |
| 6. #26018294 | C2 | semidirect |
| 7. C89×#1360 | C2 | semidirect |
| 20. C4⋊#13083549 | C22 | semidirect |
| 22. #19151349 | C22 | semidirect |
| 25. C4⋊C16×C89 | C22 | semidirect |
| 26. #334×C89 | C22 | semidirect |
| 178. D89 | #1360 | direct (N × H) |
| 185. #1360 | D89 | direct (N × H) |
| 186. C89 | C2×#1360 | semidirect |
| 202. C4⋊C16 | C2×D89 | semidirect |
| 205. #334 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #495×D89 | 2 |
| C4⋊C16×D89 | 2 |
| #334×D89 | 2 |
| #26018296 | 2 |
| #26018295 | 2 |
| #26018294 | 2 |
| C89×#1360 | 2 |
| C2×#1360 | 89 |