Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
578 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 578 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 |
|---|---|---|
| 3. #26025240 | C2 | semidirect |
| 4. #26018925 | C2 | semidirect |
| 6. #26018646 | C2 | semidirect |
| 7. C89×#1303 | C2 | semidirect |
| 218. #1303 | D89 | semidirect |
| 219. C89 | #10243 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031375 | 2 |
| #26029726 | 2 |
| #26025240 | 2 |
| #26018925 | 2 |
| #26018746 | 2 |
| #26018646 | 2 |
| C89×#1303 | 2 |
| #10243 | 89 |