Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
856 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 856 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 1. C2×#19151914 | C2 | semidirect |
| 3. C2×#19151535 | C2 | semidirect |
| 4. #26020343 | C2 | semidirect |
| 5. C2×#19151321 | C2 | semidirect |
| 6. #26018131 | C2 | semidirect |
| 7. C2×#327×C89 | C2 | semidirect |
| 46. C2×C4⋊Dic89 | D4 | semidirect |
| 61. C22⋊#10623494 | D4 | semidirect |
| 78. #95×C89 | D4 | semidirect |
| 274. C2×#327 | D89 | semidirect |
| 277. C89 | #9920 | semidirect |
| 348. #95 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151914 | 2 |
| #26025988 | 2 |
| C2×#19151535 | 2 |
| #26020343 | 2 |
| C2×#19151321 | 2 |
| #26018131 | 2 |
| C2×#327×C89 | 2 |
| #9920 | 89 |