Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
770 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 3. #26021238 | C2 | semidirect |
| 4. #26020187 | C2 | semidirect |
| 6. #26018098 | C2 | semidirect |
| 7. C2×#451×C89 | C2 | semidirect |
| 232. C2×#451 | D89 | semidirect |
| 238. C89 | #9956 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031005 | 2 |
| #26023906 | 2 |
| #26021238 | 2 |
| #26020187 | 2 |
| #26018821 | 2 |
| #26018098 | 2 |
| C2×#451×C89 | 2 |
| #9956 | 89 |