Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
878 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 878 conjugacy classes of subgroups — too many to draw. Only its 95 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. #26029291 | C2 | semidirect |
| 3. #26020172 | C2 | semidirect |
| 4. #26020172 | C2 | semidirect |
| 5. #26018588 | C2 | semidirect |
| 6. #26018158 | C2 | semidirect |
| 7. C89×#1305 | C2 | semidirect |
| 41. C2×#13083558 | D4 | semidirect |
| 67. C2×M16×C89 | D4 | semidirect |
| 190. C2×Dic89 | #100 | semidirect |
| 255. #1305 | D89 | semidirect |
| 256. C89 | #9504 | semidirect |
| 294. C2×M16 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029291 | 2 |
| #26023609 | 2 |
| #26020172 | 2 |
| #26018588 | 2 |
| #26018158 | 2 |
| C89×#1305 | 2 |
| #9504 | 89 |