Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
516 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 13. #19151393 | C4 | semidirect |
| 68. C2×Q8×C89 | C4⋊C4 | semidirect |
| 90. C42×C89 | C4⋊C4 | semidirect |
| 163. C89 | #12967 | semidirect |
| 212. C2×Q8 | #13083553 | semidirect |
| 248. C42 | #13083553 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023426 | 2 |
| C2×#19151393 | 2 |
| #26020533 | 2 |
| #26018371 | 2 |
| C89×#1885 | 2 |
| #12967 | 89 |