Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
2062 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 2062 conjugacy classes of subgroups — too many to draw. Only its 291 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. C22×#15667927 | C2 | semidirect |
| 3. C2×#19151390 | C2 | direct (N × H) |
| 4. C22×#99×C89 | C2 | semidirect |
| 5. C23×D356 | C4 | semidirect |
| 10. C2×#15668008 | C4 | semidirect |
| 13. C22×C4×Dic89 | C4 | semidirect |
| 15. C2×#15667927 | C22 | semidirect |
| 16. #19151390 | C22 | direct (N × H) |
| 20. C2×#99×C89 | C22 | semidirect |
| 25. C22×D356 | C2×C4 | semidirect |
| 37. #15668008 | C2×C4 | semidirect |
| 42. C2×C4×Dic89 | C2×C4 | semidirect |
| 44. #15667927 | C23 | semidirect |
| 58. #99×C89 | C23 | semidirect |
| 69. C2×D356 | C22×C4 | semidirect |
| 85. C4×Dic89 | C22×C4 | semidirect |
| 190. C22×C89 | #353 | semidirect |
| 211. C2×C89 | C2×#353 | semidirect |
| 216. C22×#99 | D89 | semidirect |
| 218. C89 | C22×#353 | semidirect |
| 233. C2×#99 | C2×D89 | semidirect |
| 272. #99 | C22×D89 | semidirect |
| 409. C22 | #19151390 | direct (N × H) |
| 425. C2 | C2×#19151390 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668008 | 2 |
| C22×#15667927 | 2 |
| C2×#19151390 | 2 |
| C22×#99×C89 | 2 |
| C22×#353 | 89 |