Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
512 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 107 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×#19151714 | C2 | semidirect |
| 3. #26021965 | C2 | semidirect |
| 4. #26021119 | C2 | semidirect |
| 5. #26018362 | C2 | semidirect |
| 6. #26018333 | C2 | semidirect |
| 7. C2×#361×C89 | C2 | semidirect |
| 11. #19152034 | C4 | semidirect |
| 81. Dic356 | C22⋊C4 | semidirect |
| 85. D712 | C22⋊C4 | semidirect |
| 188. C2×#361 | D89 | semidirect |
| 193. C89 | #13029 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152034 | 2 |
| C2×#19151714 | 2 |
| #26021965 | 2 |
| #26021119 | 2 |
| #26018362 | 2 |
| #26018333 | 2 |
| C2×#361×C89 | 2 |
| #13029 | 89 |