Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
390 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 390 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. #26022006 | C2 | semidirect |
| 3. #346×D89 | C2 | semidirect |
| 4. #26018211 | C2 | semidirect |
| 5. #26018210 | C2 | semidirect |
| 6. #26018209 | C2 | semidirect |
| 7. C89×#1330 | C2 | semidirect |
| 174. #1330 | D89 | semidirect |
| 175. C89 | #11588 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028961 | 2 |
| #26022006 | 2 |
| #346×D89 | 2 |
| #26018211 | 2 |
| #26018210 | 2 |
| #26018209 | 2 |
| C89×#1330 | 2 |
| #11588 | 89 |