Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
734 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 734 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 3. #26020351 | C2 | semidirect |
| 5. #26018106 | C2 | semidirect |
| 6. #26018105 | C2 | semidirect |
| 7. C89×#1826 | C2 | semidirect |
| 11. #19151533 | C4 | semidirect |
| 12. #19151524 | C4 | semidirect |
| 52. #15667919 | C2×C4 | semidirect |
| 59. C2×C4⋊C4×C89 | C2×C4 | semidirect |
| 60. C2×C4⋊C4×C89 | C2×C4 | semidirect |
| 209. #1826 | D89 | semidirect |
| 213. C89 | #9477 | semidirect |
| 244. C2×C4⋊C4 | C4×D89 | semidirect |
| 245. C2×C4⋊C4 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26024522 | 2 |
| #26022604 | 2 |
| #26020351 | 2 |
| #26018578 | 2 |
| #26018106 | 2 |
| #26018105 | 2 |
| C89×#1826 | 2 |
| #9477 | 89 |