Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
958 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 958 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. #26020197 | C2 | semidirect |
| 3. #26018579 | C2 | semidirect |
| 4. #26018105 | C2 | semidirect |
| 5. C89×#2273 | C2 | semidirect |
| 10. #19151510 | C4 | semidirect |
| 11. #19151507 | C4 | semidirect |
| 24. C22×Dic178 | C2×C4 | semidirect |
| 25. C22×D356 | C2×C4 | semidirect |
| 39. #15667919 | C2×C4 | semidirect |
| 52. C2×C42×C89 | D4 | semidirect |
| 122. C23×C89 | #104 | semidirect |
| 200. #2273 | D89 | semidirect |
| 204. C89 | #9475 | semidirect |
| 245. C2×C42 | C22⋊D89 | semidirect |
| 326. C23 | #15667940 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023571 | 2 |
| #26020197 | 2 |
| #26018579 | 2 |
| #26018105 | 2 |
| C89×#2273 | 2 |
| #9475 | 89 |