Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1958 conjugacy classes of subgroups; only the 587 normal subgroups are shown.
This group has 1958 conjugacy classes of subgroups — too many to draw. Only its 587 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. #26028438 | C2 | direct (N × H) |
| 2. C2×C89⋊#401 | C2 | semidirect |
| 3. C2×#19151531 | C2 | semidirect |
| 11. C89⋊#401 | C22 | semidirect |
| 12. #19151531 | C22 | semidirect |
| 106. C2×C89 | #2834 | semidirect |
| 116. C89 | C2×#2834 | semidirect |
| 215. C2 | #26028438 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028438 | 2 |
| C2×C89⋊#401 | 2 |
| C2×#19151531 | 2 |
| C2×#19151523 | 2 |
| C2×#19151470 | 2 |
| C2×#399×C89 | 2 |
| C2×#2834 | 89 |