Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
690 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 111 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. #26022850 | C2 | semidirect |
| 3. #26018821 | C2 | semidirect |
| 4. #26018120 | C2 | semidirect |
| 5. C2×#323×C89 | C2 | semidirect |
| 8. #19151523 | C4 | semidirect |
| 10. #19151507 | C4 | semidirect |
| 41. #15667919 | D4 | semidirect |
| 191. C2×#323 | D89 | semidirect |
| 193. C89 | #9205 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025986 | 2 |
| #26022850 | 2 |
| #26018821 | 2 |
| #26018120 | 2 |
| C2×#323×C89 | 2 |
| #9205 | 89 |