Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
342 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 123 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×#19151424 | C2 | semidirect |
| 3. #26018431 | C2 | direct (N × H) |
| 4. C22×C32×C89 | C2 | semidirect |
| 8. C2×D1424 | C4 | semidirect |
| 12. #19151424 | C22 | semidirect |
| 15. C2×C32×C89 | C22 | semidirect |
| 24. D1424 | C2×C4 | semidirect |
| 82. C2×C89 | #1415 | semidirect |
| 88. C22×C32 | D89 | semidirect |
| 91. C89 | C2×#1415 | semidirect |
| 100. C2×C32 | C2×D89 | semidirect |
| 169. C2 | #26018431 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1424 | 2 |
| C2×#19151424 | 2 |
| #26018431 | 2 |
| C22×C32×C89 | 2 |
| C2×#1415 | 89 |