Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1854 conjugacy classes of subgroups; only the 331 normal subgroups are shown.
This group has 1854 conjugacy classes of subgroups — too many to draw. Only its 331 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. C2×#19151462 | C2 | semidirect |
| 3. #26018522 | C2 | semidirect |
| 4. #26018495 | C2 | semidirect |
| 9. C2×#15667999 | C4 | semidirect |
| 68. C4×Dic89 | C22⋊C4 | semidirect |
| 164. C89 | #14662 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15667999 | 2 |
| C2×#19151462 | 2 |
| #26018522 | 2 |
| #26018495 | 2 |
| #26018493 | 2 |
| C89×#1438 | 2 |
| #14662 | 89 |