Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
752 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 103 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×#19151582 | C2 | semidirect |
| 3. C2×#19151394 | C2 | semidirect |
| 4. #26018378 | C2 | semidirect |
| 5. C89×#1785 | C2 | semidirect |
| 49. #15667931 | D4 | semidirect |
| 260. #1785 | D89 | semidirect |
| 262. C89 | #13093 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151582 | 2 |
| #26023867 | 2 |
| C2×#19151394 | 2 |
| #26018378 | 2 |
| C89×#1785 | 2 |
| #13093 | 89 |