Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
474 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 4. C2×#19151402 | C2 | semidirect |
| 5. #26018362 | C2 | semidirect |
| 6. #26018341 | C2 | semidirect |
| 7. C89×#1979 | C2 | semidirect |
| 11. #19152039 | C4 | semidirect |
| 45. #15667952 | C2×C4 | semidirect |
| 60. C2×Q16×C89 | C2×C4 | semidirect |
| 186. #1979 | D89 | semidirect |
| 189. C89 | #13023 | semidirect |
| 222. C2×Q16 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152039 | 2 |
| #26029129 | 2 |
| C2×#19151404 | 2 |
| C2×#19151402 | 2 |
| #26018362 | 2 |
| #26018341 | 2 |
| C89×#1979 | 2 |
| #13023 | 89 |