Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
558 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 558 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×#19152039 | C2 | semidirect |
| 3. C2×#19151407 | C2 | semidirect |
| 4. #26018336 | C2 | semidirect |
| 5. C89×#1971 | C2 | semidirect |
| 43. #15667952 | D4 | semidirect |
| 49. C2×Q16×C89 | D4 | semidirect |
| 157. #1971 | D89 | semidirect |
| 159. C89 | #13342 | semidirect |
| 189. C2×Q16 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152039 | 2 |
| #26030698 | 2 |
| C2×#19151407 | 2 |
| #26018336 | 2 |
| C89×#1971 | 2 |
| #13342 | 89 |