Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
660 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 660 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 |
|---|---|---|
| 10. #19151528 | C4 | semidirect |
| 175. C89 | #9027 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151528 | 2 |
| #26020336 | 2 |
| C2×#19151324 | 2 |
| #26018130 | 2 |
| C89×#2316 | 2 |
| #9027 | 89 |