Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
800 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 147 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 |
|---|---|---|
| 11. #19151518 | C4 | semidirect |
| 124. C2×C4×C89 | #103 | semidirect |
| 180. C89 | #9015 | semidirect |
| 312. C2×C4 | #15667935 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151518 | 2 |
| #26020186 | 2 |
| C2×#19151324 | 2 |
| #26018130 | 2 |
| C89×#2316 | 2 |
| #9015 | 89 |