Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
326 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 95 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×#19151427 | C2 | semidirect |
| 2. #26022011 | C2 | semidirect |
| 6. #26018360 | C2 | semidirect |
| 7. C89×#1952 | C2 | semidirect |
| 147. #1952 | D89 | semidirect |
| 149. C89 | #13470 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151427 | 2 |
| #26022011 | 2 |
| C2×#19151410 | 2 |
| C2×#19151398 | 2 |
| #26021162 | 2 |
| #26018360 | 2 |
| C89×#1952 | 2 |
| #13470 | 89 |