Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
604 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 171 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×#19151647 | C2 | semidirect |
| 3. #26022467 | C2 | direct (N × H) |
| 4. C2×#19151421 | C2 | semidirect |
| 5. C2×#19151412 | C2 | semidirect |
| 6. C2×#349×C89 | C2 | semidirect |
| 13. #19151647 | C22 | semidirect |
| 18. #19151421 | C22 | semidirect |
| 19. #19151412 | C22 | semidirect |
| 22. #349×C89 | C22 | semidirect |
| 150. C2×C89 | #2238 | semidirect |
| 158. C2×#349 | D89 | semidirect |
| 159. C89 | C2×#2238 | semidirect |
| 175. #349 | C2×D89 | semidirect |
| 303. C2 | #26022467 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151851 | 2 |
| C2×#19151647 | 2 |
| #26022467 | 2 |
| C2×#19151421 | 2 |
| C2×#19151412 | 2 |
| C2×#349×C89 | 2 |
| C2×#2238 | 89 |