Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
342 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 47 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 |
|---|---|---|
| 1. #26018186 | C2 | semidirect |
| 2. #26018078 | C2 | semidirect |
| 16. 2−1+4×C89 | C8 | semidirect |
| 132. C89 | #7345 | semidirect |
| 143. 2−1+4 | #10623494 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26018186 | 2 |
| #26018078 | 2 |
| C89×#1793 | 2 |
| #7345 | 89 |