Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
648 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 127 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×#19151466 | C2 | semidirect |
| 4. #26018132 | C2 | semidirect |
| 5. C89×#1817 | C2 | semidirect |
| 8. #19151500 | C4 | semidirect |
| 9. #19151496 | C4 | semidirect |
| 169. #1817 | D89 | semidirect |
| 172. C89 | #9157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028583 | 2 |
| C2×#19151466 | 2 |
| C2×#19151333 | 2 |
| #26018132 | 2 |
| C89×#1817 | 2 |
| #9157 | 89 |