Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
486 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 83 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. C4×#15667927 | C2 | semidirect |
| 3. #26018277 | C2 | semidirect |
| 4. #26018250 | C2 | semidirect |
| 5. C89×#1460 | C2 | semidirect |
| 6. C2×#15667986 | C4 | semidirect |
| 8. #19151537 | C4 | semidirect |
| 10. #19151515 | C4 | semidirect |
| 16. #19151461 | C4 | semidirect |
| 198. #1460 | D89 | semidirect |
| 201. C89 | #11729 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26026136 | 2 |
| C4×#15667927 | 2 |
| #26018277 | 2 |
| #26018250 | 2 |
| C89×#1460 | 2 |
| #11729 | 89 |