Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
334 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 89 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. #26019026 | C2 | semidirect |
| 3. #26019022 | C2 | semidirect |
| 6. #26018081 | C2 | semidirect |
| 7. C89×#1832 | C2 | semidirect |
| 130. #1832 | D89 | semidirect |
| 136. C89 | #10665 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021084 | 2 |
| #26019026 | 2 |
| #26019022 | 2 |
| #26018650 | 2 |
| #26018081 | 2 |
| C89×#1832 | 2 |
| #10665 | 89 |