Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
286 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 107 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. #26018446 | C2 | direct (N × H) |
| 97. C2×C89 | #1420 | semidirect |
| 103. C89 | C2×#1420 | semidirect |
| 195. C2 | #26018446 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic712 | 2 |
| C2×#19151428 | 2 |
| #26018446 | 2 |
| C2×M64×C89 | 2 |
| C2×#1420 | 89 |