Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
206 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 2. #26018452 | C2 | direct (N × H) |
| 8. C2×C32×C89 | C4 | semidirect |
| 18. C32×C89 | C2×C4 | semidirect |
| 49. C2×C89 | #1423 | semidirect |
| 56. C89 | C2×#1423 | semidirect |
| 59. C2×C32 | Dic89 | semidirect |
| 71. C32 | C2×Dic89 | semidirect |
| 101. C2 | #26018452 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151424 | 2 |
| #26018452 | 2 |
| C22×C32×C89 | 2 |
| C2×#1423 | 89 |