Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
714 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 714 conjugacy classes of subgroups — too many to draw. Only its 187 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 |
|---|---|---|
| 144. C89 | #23825 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15668012 | 2 |
| C4×#15668004 | 2 |
| #26021816 | 2 |
| #26021672 | 2 |
| #26021499 | 2 |
| #26021404 | 2 |
| #26020083 | 2 |
| C89×#1745 | 2 |
| #23825 | 89 |