Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
500 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 500 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. #26021979 | C2 | semidirect |
| 3. C2×#19151380 | C2 | semidirect |
| 4. #26018366 | C2 | semidirect |
| 5. C2×#430×C89 | C2 | semidirect |
| 54. #108×C89 | D4 | semidirect |
| 156. C2×#430 | D89 | semidirect |
| 160. C89 | #12998 | semidirect |
| 205. #108 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029861 | 2 |
| #26021979 | 2 |
| C2×#19151380 | 2 |
| #26018366 | 2 |
| C2×#430×C89 | 2 |
| #12998 | 89 |