Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
744 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 744 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 138. C22⋊C4×C89 | Q16 | semidirect |
| 227. C89 | #9957 | semidirect |
| 358. C22⋊C4 | #13083564 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031024 | 2 |
| C2×#19151753 | 2 |
| #26023896 | 2 |
| #26020186 | 2 |
| #26018823 | 2 |
| #26018100 | 2 |
| C89×#1996 | 2 |
| #9957 | 89 |