Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
436 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 68. C2×Dic178 | Q16 | semidirect |
| 110. C4⋊C4×C89 | Q16 | semidirect |
| 192. C89 | #7784 | semidirect |
| 294. C4⋊C4 | #13083564 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028214 | 2 |
| #26021390 | 2 |
| #26021352 | 2 |
| #26018077 | 2 |
| #26018075 | 2 |
| C89×#2057 | 2 |
| #7784 | 89 |