Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
954 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 954 conjugacy classes of subgroups — too many to draw. Only its 155 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×#19151403 | C2 | semidirect |
| 3. C2×#19151400 | C2 | semidirect |
| 4. #26020281 | C2 | semidirect |
| 5. C2×C22⋊C16×C89 | C2 | semidirect |
| 10. C2×#15668034 | C4 | semidirect |
| 78. Dic356 | C22⋊C4 | semidirect |
| 82. D712 | C22⋊C4 | semidirect |
| 172. C2×C22⋊C16 | D89 | semidirect |
| 174. C89 | #12733 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668034 | 2 |
| C2×#19151403 | 2 |
| C2×#19151400 | 2 |
| #26020281 | 2 |
| C2×C22⋊C16×C89 | 2 |
| #12733 | 89 |