Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
762 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 762 conjugacy classes of subgroups — too many to draw. Only its 127 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. #26022866 | C2 | semidirect |
| 3. #26018821 | C2 | semidirect |
| 4. #26018120 | C2 | semidirect |
| 5. C2×#323×C89 | C2 | semidirect |
| 9. #19151523 | C4 | semidirect |
| 11. #19151507 | C4 | semidirect |
| 21. C22×D356 | C2×C4 | semidirect |
| 32. C2×C4⋊Dic89 | C2×C4 | semidirect |
| 43. #15667919 | C2×C4 | semidirect |
| 44. #15667919 | D4 | semidirect |
| 218. C2×#323 | D89 | semidirect |
| 220. C89 | #9203 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025986 | 2 |
| #26022866 | 2 |
| #26018821 | 2 |
| #26018120 | 2 |
| C2×#323×C89 | 2 |
| #9203 | 89 |