Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
222 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 222 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 |
|---|---|---|
| 24. M32×C89 | C8 | semidirect |
| 87. C89 | #7159 | semidirect |
| 103. M32 | #10623494 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26019000 | 2 |
| C2×#19151351 | 2 |
| C4×M32×C89 | 2 |
| #7159 | 89 |