Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
566 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×#19152039 | C2 | semidirect |
| 2. C22×#15667955 | C2 | semidirect |
| 4. C2×#19151410 | C2 | semidirect |
| 5. C2×#19151404 | C2 | semidirect |
| 6. #26018341 | C2 | semidirect |
| 7. C89×#1979 | C2 | semidirect |
| 58. #15667952 | D4 | semidirect |
| 62. C2×#13083549 | D4 | semidirect |
| 69. C2×Q16×C89 | D4 | semidirect |
| 207. #1979 | D89 | semidirect |
| 209. C89 | #13338 | semidirect |
| 248. C2×Q16 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152039 | 2 |
| C22×#15667955 | 2 |
| #26030738 | 2 |
| C2×#19151410 | 2 |
| C2×#19151404 | 2 |
| #26018341 | 2 |
| C89×#1979 | 2 |
| #13338 | 89 |