Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
808 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 808 conjugacy classes of subgroups — too many to draw. Only its 155 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 |
|---|---|---|
| 1. C2×C89⋊#564 | C2 | semidirect |
| 4. #26019581 | C2 | semidirect |
| 5. #26019555 | C2 | semidirect |
| 6. #26018855 | C2 | semidirect |
| 7. C89×#1534 | C2 | semidirect |
| 152. #1534 | D89 | semidirect |
| 154. C89 | #19003 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C89⋊#564 | 2 |
| #26031444 | 2 |
| #26030655 | 2 |
| #26019581 | 2 |
| #26019555 | 2 |
| #26018855 | 2 |
| C89×#1534 | 2 |
| #19003 | 89 |