Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
354 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 119 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×#19151428 | C2 | semidirect |
| 4. #26018355 | C2 | semidirect |
| 5. C2×#368×C89 | C2 | semidirect |
| 119. C2×#368 | D89 | semidirect |
| 122. C89 | #12840 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152014 | 2 |
| C2×#19151428 | 2 |
| #26020299 | 2 |
| #26018355 | 2 |
| C2×#368×C89 | 2 |
| #12840 | 89 |