Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
648 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 107 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. #26023299 | C2 | semidirect |
| 3. #26021089 | C2 | semidirect |
| 4. #26018821 | C2 | semidirect |
| 5. #26018131 | C2 | semidirect |
| 6. #26018099 | C2 | semidirect |
| 7. C2×#327×C89 | C2 | semidirect |
| 10. #19151911 | C4 | semidirect |
| 13. #19151732 | C4 | semidirect |
| 60. C22⋊#10623494 | C2×C4 | semidirect |
| 66. C22×D4×C89 | C2×C4 | semidirect |
| 74. C2×C4⋊C4×C89 | C2×C4 | semidirect |
| 110. C22⋊Dic89 | D8 | semidirect |
| 274. C2×#327 | D89 | semidirect |
| 277. C89 | #9277 | semidirect |
| 304. C22×D4 | C4×D89 | semidirect |
| 324. C2×C4⋊C4 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031000 | 2 |
| #26023299 | 2 |
| #26021089 | 2 |
| #26018821 | 2 |
| #26018131 | 2 |
| #26018099 | 2 |
| C2×#327×C89 | 2 |
| #9277 | 89 |