Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
468 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 135. C4×C89 | #356 | semidirect |
| 146. C89 | #12802 | semidirect |
| 277. C4 | #19151397 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151397 | 2 |
| #26020248 | 2 |
| #26018379 | 2 |
| C4×C4⋊Q8×C89 | 2 |
| #12802 | 89 |