Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
496 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 243. C89 | #13421 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26027180 | 2 |
| C2×#19151388 | 2 |
| C2×#19151387 | 2 |
| #26020665 | 2 |
| #26020462 | 2 |
| #26018376 | 2 |
| C89×#1890 | 2 |
| #13421 | 89 |