Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
648 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 109 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. #26023302 | C2 | semidirect |
| 3. #26021088 | C2 | semidirect |
| 4. #26018821 | C2 | semidirect |
| 5. C2×#19151333 | C2 | semidirect |
| 6. #26018132 | C2 | semidirect |
| 7. C89×#1282 | C2 | semidirect |
| 12. #19151912 | C4 | semidirect |
| 15. #19151734 | C4 | semidirect |
| 31. C22×D356 | C2×C4 | semidirect |
| 49. C2×C4⋊Dic89 | C2×C4 | semidirect |
| 79. C22⋊C8×C89 | C2×C4 | semidirect |
| 147. C22⋊C4×C89 | D8 | semidirect |
| 276. #1282 | D89 | semidirect |
| 277. C89 | #9277 | semidirect |
| 343. C22⋊C8 | C4×D89 | semidirect |
| 416. C22⋊C4 | D712 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031003 | 2 |
| #26023302 | 2 |
| #26021088 | 2 |
| #26018821 | 2 |
| C2×#19151333 | 2 |
| #26018132 | 2 |
| C89×#1282 | 2 |
| #9277 | 89 |