Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
984 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 984 conjugacy classes of subgroups — too many to draw. Only its 203 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 |
|---|---|---|
| 4. #26019296 | C2 | direct (N × H) |
| 183. C2×C89 | #1617 | semidirect |
| 193. C89 | C2×#1617 | semidirect |
| 369. C2 | #26019296 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152229 | 2 |
| C2×#19151934 | 2 |
| C2×#19151537 | 2 |
| #26019296 | 2 |
| C2×#19151336 | 2 |
| C2×#324×C89 | 2 |
| C2×#1617 | 89 |