Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
424 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 107. C4⋊C4×C89 | Q16 | semidirect |
| 188. C89 | #7783 | semidirect |
| 288. C4⋊C4 | #13083564 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021585 | 2 |
| #26021580 | 2 |
| #26021351 | 2 |
| #26018078 | 2 |
| #26018075 | 2 |
| C89×#2805 | 2 |
| #7783 | 89 |