Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
508 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26018277 | C2 | semidirect |
| 5. C2×#15668012 | C4 | semidirect |
| 9. #19151534 | C4 | semidirect |
| 14. C4×C4⋊Dic89 | C4 | semidirect |
| 173. C89 | #11901 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025205 | 2 |
| #26020240 | 2 |
| #26018277 | 2 |
| C89×#1459 | 2 |
| #11901 | 89 |