Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
784 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 784 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. #26020195 | C2 | semidirect |
| 3. C4×#15667927 | C2 | semidirect |
| 4. #26018137 | C2 | semidirect |
| 5. C89×#2973 | C2 | semidirect |
| 10. #19151518 | C4 | semidirect |
| 11. #19151515 | C4 | semidirect |
| 13. #19151510 | C4 | semidirect |
| 14. #19151507 | C4 | semidirect |
| 53. C2×M16×C89 | D4 | semidirect |
| 131. C23×C89 | #104 | semidirect |
| 220. #2973 | D89 | semidirect |
| 225. C89 | #9009 | semidirect |
| 256. C2×M16 | C22⋊D89 | semidirect |
| 358. C23 | #15667938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023467 | 2 |
| #26020195 | 2 |
| C4×#15667927 | 2 |
| #26018137 | 2 |
| C89×#2973 | 2 |
| #9009 | 89 |