Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
270 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 67 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×D2848 | C2 | semidirect |
| 2. C2×#19151433 | C2 | semidirect |
| 3. #26022500 | C2 | semidirect |
| 4. C32×Dic89 | C2 | semidirect |
| 5. C2×D32×C89 | C2 | semidirect |
| 24. #15667918 | D4 | semidirect |
| 29. C32×C89 | D4 | semidirect |
| 63. Dic89 | D32 | semidirect |
| 71. C2×D32 | D89 | semidirect |
| 74. C89 | #13725 | semidirect |
| 98. C32 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D2848 | 2 |
| C2×#19151433 | 2 |
| #26022500 | 2 |
| C32×Dic89 | 2 |
| C2×D32×C89 | 2 |
| #13725 | 89 |