Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
958 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 958 conjugacy classes of subgroups — too many to draw. Only its 97 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. #26022604 | C2 | semidirect |
| 3. #26020196 | C2 | semidirect |
| 4. #26018578 | C2 | semidirect |
| 5. #26018106 | C2 | semidirect |
| 6. #26018105 | C2 | semidirect |
| 7. C89×#1789 | C2 | semidirect |
| 13. #19151509 | C4 | semidirect |
| 14. #19151506 | C4 | semidirect |
| 46. C2×C4×Dic89 | D4 | semidirect |
| 54. #15667919 | C2×C4 | semidirect |
| 60. C22×Q8×C89 | C2×C4 | semidirect |
| 62. C22×D4×C89 | C2×C4 | semidirect |
| 67. C2×C42×C89 | D4 | semidirect |
| 163. C22×D89 | #104 | semidirect |
| 251. #1789 | D89 | semidirect |
| 255. C89 | #9475 | semidirect |
| 281. C22×Q8 | C4×D89 | semidirect |
| 284. C22×D4 | C4×D89 | semidirect |
| 307. C2×C42 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023567 | 2 |
| #26022604 | 2 |
| #26020196 | 2 |
| #26018578 | 2 |
| #26018106 | 2 |
| #26018105 | 2 |
| C89×#1789 | 2 |
| #9475 | 89 |