Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
866 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 866 conjugacy classes of subgroups — too many to draw. Only its 251 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×#19151996 | C2 | semidirect |
| 2. C2×#19151950 | C2 | semidirect |
| 4. #26019851 | C2 | direct (N × H) |
| 5. C2×C8×#10623494 | C2 | semidirect |
| 9. #19151996 | C22 | semidirect |
| 11. #19151950 | C22 | semidirect |
| 18. C8×#10623494 | C22 | semidirect |
| 123. C2×C89 | #1708 | semidirect |
| 132. C89 | C2×#1708 | semidirect |
| 248. C2 | #26019851 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151996 | 2 |
| C2×#19151950 | 2 |
| C2×#19151944 | 2 |
| #26019851 | 2 |
| C2×C8×#10623494 | 2 |
| C2×#492×C89 | 2 |
| C2×#1708 | 89 |