Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1074 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 1074 conjugacy classes of subgroups — too many to draw. Only its 219 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×#19151893 | C2 | semidirect |
| 3. #26019373 | C2 | direct (N × H) |
| 5. C2×Q8⋊#10623494 | C2 | semidirect |
| 12. #19151893 | C22 | semidirect |
| 18. Q8⋊#10623494 | C22 | semidirect |
| 151. C2×C89 | #1630 | semidirect |
| 160. C89 | C2×#1630 | semidirect |
| 304. C2 | #26019373 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151970 | 2 |
| C2×#19151893 | 2 |
| #26019373 | 2 |
| C2×#19151342 | 2 |
| C2×Q8⋊#10623494 | 2 |
| C2×#559×C89 | 2 |
| C2×#1630 | 89 |