Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
534 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 534 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. #26018802 | C2 | semidirect |
| 4. #26018116 | C2 | semidirect |
| 8. #19151944 | C4 | semidirect |
| 19. #15668012 | C2×C4 | semidirect |
| 29. C4×#10623494 | C2×C4 | semidirect |
| 117. C89 | #9425 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030626 | 2 |
| #26018966 | 2 |
| #26018802 | 2 |
| #26018116 | 2 |
| C89×#2380 | 2 |
| #9425 | 89 |