Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
902 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 902 conjugacy classes of subgroups — too many to draw. Only its 143 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. C2×#19151335 | C2 | semidirect |
| 4. #26018130 | C2 | semidirect |
| 14. C2×C22⋊Q8×C89 | C4 | semidirect |
| 18. #380×C89 | C4 | semidirect |
| 192. C89 | #9154 | semidirect |
| 194. C2×C22⋊Q8 | Dic89 | semidirect |
| 202. #380 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151461 | 2 |
| #26020162 | 2 |
| C2×#19151335 | 2 |
| #26018130 | 2 |
| C89×#2848 | 2 |
| #9154 | 89 |