Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
334 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 1. C22×D1424 | C2 | semidirect |
| 2. C2×#19151433 | C2 | semidirect |
| 3. #26018429 | C2 | semidirect |
| 4. C22⋊#15667918 | C2 | semidirect |
| 5. C89×#2215 | C2 | semidirect |
| 11. C2×#15667918 | C22 | semidirect |
| 12. C2×D16×C89 | C22 | semidirect |
| 15. #366×C89 | C22 | semidirect |
| 24. D1424 | D4 | semidirect |
| 81. C22×C89 | D32 | semidirect |
| 100. #2215 | D89 | semidirect |
| 103. C89 | #13661 | semidirect |
| 108. C2×D16 | C2×D89 | semidirect |
| 113. #366 | C2×D89 | semidirect |
| 183. C22 | #19151433 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1424 | 2 |
| C2×#19151433 | 2 |
| #26018429 | 2 |
| C22⋊#15667918 | 2 |
| C89×#2215 | 2 |
| #13661 | 89 |