Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
380 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 109 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×#19151420 | C2 | semidirect |
| 5. #26018364 | C2 | semidirect |
| 6. #26018355 | C2 | semidirect |
| 7. C2×#365×C89 | C2 | semidirect |
| 18. #19151383 | C4 | semidirect |
| 142. C2×#365 | D89 | semidirect |
| 147. C89 | #12933 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028860 | 2 |
| C2×#19151420 | 2 |
| #26021881 | 2 |
| #26020312 | 2 |
| #26018364 | 2 |
| #26018355 | 2 |
| C2×#365×C89 | 2 |
| #12933 | 89 |