Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
470 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 470 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 |
|---|---|---|
| 1. C2×#19152030 | C2 | semidirect |
| 2. #26022561 | C2 | direct (N × H) |
| 3. C2×Dic1424 | C2 | semidirect |
| 4. C2×#19151437 | C2 | semidirect |
| 5. C2×D2848 | C2 | semidirect |
| 6. C22×C32×C89 | C2 | semidirect |
| 9. #19152030 | C22 | semidirect |
| 13. Dic1424 | C22 | semidirect |
| 14. #19151437 | C22 | semidirect |
| 15. D2848 | C22 | semidirect |
| 19. C2×C32×C89 | C22 | semidirect |
| 84. C2×C89 | #2262 | semidirect |
| 92. C22×C32 | D89 | semidirect |
| 93. C89 | C2×#2262 | semidirect |
| 106. C2×C32 | C2×D89 | semidirect |
| 171. C2 | #26022561 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152030 | 2 |
| #26022561 | 2 |
| C2×Dic1424 | 2 |
| C2×#19151437 | 2 |
| C2×D2848 | 2 |
| C22×C32×C89 | 2 |
| C2×#2262 | 89 |