Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
316 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 28. #15667952 | Q8 | semidirect |
| 108. C89 | #13270 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029184 | 2 |
| #26021857 | 2 |
| #26018337 | 2 |
| #26018333 | 2 |
| C89×#2153 | 2 |
| #13270 | 89 |