Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
716 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 113 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. #26020567 | C2 | semidirect |
| 3. C2×#19151333 | C2 | semidirect |
| 4. #26018508 | C2 | semidirect |
| 5. C89×#1280 | C2 | semidirect |
| 46. #15667919 | D4 | semidirect |
| 231. #1280 | D89 | semidirect |
| 232. C89 | #10403 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26026354 | 2 |
| #26020567 | 2 |
| C2×#19151333 | 2 |
| #26018508 | 2 |
| C89×#1280 | 2 |
| #10403 | 89 |