Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1480 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 1480 conjugacy classes of subgroups — too many to draw. Only its 203 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. C2×#19151912 | C2 | semidirect |
| 3. C2×#19151523 | C2 | semidirect |
| 4. #26019240 | C2 | direct (N × H) |
| 5. C2×#19151333 | C2 | semidirect |
| 6. C2×#323×C89 | C2 | semidirect |
| 15. C22×C4⋊Dic89 | C22 | semidirect |
| 18. #19151912 | C22 | semidirect |
| 22. #19151523 | C22 | semidirect |
| 24. C2×#15667919 | C22 | semidirect |
| 25. #19151333 | C22 | semidirect |
| 27. C2×C22⋊C8×C89 | C22 | semidirect |
| 28. #323×C89 | C22 | semidirect |
| 56. C2×C4⋊Dic89 | C23 | semidirect |
| 65. #15667919 | C23 | semidirect |
| 75. C22⋊C8×C89 | C23 | semidirect |
| 231. C2×C89 | #1607 | semidirect |
| 241. C2×#323 | D89 | semidirect |
| 242. C89 | C2×#1607 | semidirect |
| 258. C2×C22⋊C8 | C2×D89 | semidirect |
| 264. #323 | C2×D89 | semidirect |
| 308. C22⋊C8 | C22×D89 | semidirect |
| 467. C2 | #26019240 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152160 | 2 |
| C2×#19151912 | 2 |
| C2×#19151523 | 2 |
| #26019240 | 2 |
| C2×#19151333 | 2 |
| C2×#323×C89 | 2 |
| C2×#1607 | 89 |