Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
212 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 3. C4⋊#15667918 | C2 | semidirect |
| 4. #26018433 | C2 | semidirect |
| 5. C89×#2247 | C2 | semidirect |
| 70. C4×C89 | SD64 | semidirect |
| 80. #2247 | D89 | semidirect |
| 84. C89 | #13687 | semidirect |
| 150. C4 | #19151435 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151435 | 2 |
| C4×D1424 | 2 |
| C4⋊#15667918 | 2 |
| #26018433 | 2 |
| C89×#2247 | 2 |
| #13687 | 89 |