Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
272 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 71. Q16×C89 | Q16 | semidirect |
| 137. C89 | #12415 | semidirect |
| 196. Q16 | #13083564 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022539 | 2 |
| #26022404 | 2 |
| #26019770 | 2 |
| #26018304 | 2 |
| #26018234 | 2 |
| #26018222 | 2 |
| C89×#3390 | 2 |
| #12415 | 89 |