Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1136 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1136 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. #26022282 | C2 | direct (N × H) |
| 3. C2×#19151397 | C2 | semidirect |
| 4. C2×Q82×C89 | C2 | semidirect |
| 11. #19151397 | C22 | semidirect |
| 13. Q82×C89 | C22 | semidirect |
| 126. C2×C89 | #2205 | semidirect |
| 129. C2×Q82 | D89 | semidirect |
| 133. C89 | C2×#2205 | semidirect |
| 137. Q82 | C2×D89 | semidirect |
| 255. C2 | #26022282 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151780 | 2 |
| #26022282 | 2 |
| C2×#19151397 | 2 |
| C2×Q82×C89 | 2 |
| C2×#2205 | 89 |