Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1386 conjugacy classes of subgroups; only the 243 normal subgroups are shown.
This group has 1386 conjugacy classes of subgroups — too many to draw. Only its 243 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. #26028881 | C2 | semidirect |
| 3. #26021100 | C2 | semidirect |
| 4. #26020176 | C2 | semidirect |
| 6. C89×#1784 | C2 | semidirect |
| 16. #19151621 | C22 | semidirect |
| 17. C2×#15667931 | C22 | semidirect |
| 20. M16×Dic89 | C22 | semidirect |
| 22. C2×#101×C89 | C22 | semidirect |
| 158. #1784 | D89 | semidirect |
| 160. C89 | #21798 | semidirect |
| 173. C2×#101 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668001 | 2 |
| #26028881 | 2 |
| #26021100 | 2 |
| #26020176 | 2 |
| #26020172 | 2 |
| C89×#1784 | 2 |
| #21798 | 89 |