Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
496 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 81 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. #349×D89 | C2 | semidirect |
| 3. H(3,ℤ/4)×D89 | C2 | semidirect |
| 4. #26018238 | C2 | semidirect |
| 5. #26018237 | C2 | semidirect |
| 6. #26018236 | C2 | semidirect |
| 7. C89×#1339 | C2 | semidirect |
| 8. C2×D8×D89 | C4 | semidirect |
| 13. #19151852 | C4 | semidirect |
| 17. #19151848 | C4 | semidirect |
| 18. #106×D89 | C4 | semidirect |
| 20. #19151380 | C22 | semidirect |
| 22. #19151355 | C22 | semidirect |
| 25. #349×C89 | C22 | semidirect |
| 26. H(3,ℤ/4)×C89 | C22 | semidirect |
| 30. C2×D712 | C2×C4 | semidirect |
| 58. #15667944 | C2×C4 | semidirect |
| 63. C2×D8×C89 | C2×C4 | semidirect |
| 68. #106×C89 | C2×C4 | semidirect |
| 215. D89 | #1339 | direct (N × H) |
| 222. #1339 | D89 | direct (N × H) |
| 223. C89 | C2×#1339 | semidirect |
| 239. #349 | C2×D89 | semidirect |
| 242. H(3,ℤ/4) | C2×D89 | semidirect |
| 250. C2×D8 | C4×D89 | semidirect |
| 281. #106 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #469×D89 | 2 |
| #349×D89 | 2 |
| H(3,ℤ/4)×D89 | 2 |
| #26018238 | 2 |
| #26018237 | 2 |
| #26018236 | 2 |
| C89×#1339 | 2 |
| C2×#1339 | 89 |