Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
386 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 2. #26021863 | C2 | semidirect |
| 3. #26018193 | C2 | semidirect |
| 4. #26018177 | C2 | semidirect |
| 5. C89×#2112 | C2 | semidirect |
| 171. #2112 | D89 | semidirect |
| 174. C89 | #11469 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028946 | 2 |
| #26021863 | 2 |
| #26018193 | 2 |
| #26018177 | 2 |
| C89×#2112 | 2 |
| #11469 | 89 |