Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
512 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 75 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×#19151394 | C2 | semidirect |
| 3. #26020656 | C2 | semidirect |
| 4. #26020653 | C2 | semidirect |
| 5. #26020469 | C2 | semidirect |
| 6. #26018378 | C2 | semidirect |
| 7. C2×#355×C89 | C2 | semidirect |
| 77. #101×C89 | D4 | semidirect |
| 240. C2×#355 | D89 | semidirect |
| 245. C89 | #13426 | semidirect |
| 312. #101 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26027276 | 2 |
| C2×#19151394 | 2 |
| #26020656 | 2 |
| #26020653 | 2 |
| #26020469 | 2 |
| #26018378 | 2 |
| C2×#355×C89 | 2 |
| #13426 | 89 |