Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
524 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 6. C2×Q8×Dic89 | C4 | semidirect |
| 9. #19151505 | C4 | semidirect |
| 13. #19151468 | C4 | semidirect |
| 15. #19151444 | C4 | semidirect |
| 76. C2×Q8×C89 | C4⋊C4 | semidirect |
| 91. C42×C89 | C4⋊C4 | semidirect |
| 169. C89 | #12800 | semidirect |
| 219. C2×Q8 | #13083553 | semidirect |
| 255. C42 | #13083553 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022965 | 2 |
| C2×#19151393 | 2 |
| #26020238 | 2 |
| #26018376 | 2 |
| C2×#354×C89 | 2 |
| #12800 | 89 |