Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
908 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 147 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. #26020186 | C2 | semidirect |
| 4. #26018130 | C2 | semidirect |
| 11. #19151510 | C4 | semidirect |
| 24. C22×Dic178 | C2×C4 | semidirect |
| 35. #15667919 | C2×C4 | semidirect |
| 120. C23×C89 | #103 | semidirect |
| 204. C89 | #9013 | semidirect |
| 319. C23 | #15667935 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151510 | 2 |
| #26020186 | 2 |
| C2×#19151322 | 2 |
| #26018130 | 2 |
| C89×#2315 | 2 |
| #9013 | 89 |