Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
406 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 3. #26019011 | C2 | semidirect |
| 4. #26018942 | C2 | semidirect |
| 6. #26018126 | C2 | semidirect |
| 7. C89×#1493 | C2 | semidirect |
| 186. #1493 | D89 | semidirect |
| 189. C89 | #10461 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030045 | 2 |
| #26020241 | 2 |
| #26019011 | 2 |
| #26018942 | 2 |
| C2×#19151327 | 2 |
| #26018126 | 2 |
| C89×#1493 | 2 |
| #10461 | 89 |