Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
370 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 21. C2×Dic356 | Q8 | semidirect |
| 117. C89 | #13368 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030776 | 2 |
| #26021973 | 2 |
| #26021123 | 2 |
| #26018358 | 2 |
| C89×#1377 | 2 |
| #13368 | 89 |