Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
370 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 90. C22×C4×C89 | Q16 | semidirect |
| 186. C89 | #12219 | semidirect |
| 258. C22×C4 | #13083564 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021419 | 2 |
| #26019276 | 2 |
| #26019208 | 2 |
| #26018276 | 2 |
| #26018273 | 2 |
| #26018182 | 2 |
| C89×#2841 | 2 |
| #12219 | 89 |