Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
620 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 83 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×#19151322 | C2 | semidirect |
| 3. #26018275 | C2 | semidirect |
| 4. #26018248 | C2 | semidirect |
| 5. C89×#1819 | C2 | semidirect |
| 7. C2×#15667986 | C4 | semidirect |
| 10. #19151534 | C4 | semidirect |
| 12. #19151507 | C4 | semidirect |
| 16. C4×C22⋊Dic89 | C4 | semidirect |
| 228. #1819 | D89 | semidirect |
| 232. C89 | #11843 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025183 | 2 |
| C2×#19151322 | 2 |
| #26018275 | 2 |
| #26018248 | 2 |
| C89×#1819 | 2 |
| #11843 | 89 |