Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1630 conjugacy classes of subgroups; only the 283 normal subgroups are shown.
This group has 1630 conjugacy classes of subgroups — too many to draw. Only its 283 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. #26022906 | C2 | semidirect |
| 3. #26020660 | C2 | semidirect |
| 4. #26020533 | C2 | semidirect |
| 5. #26020200 | C2 | semidirect |
| 6. C4×#15667927 | C2 | semidirect |
| 7. C4×H(5,𝔽2)×C89 | C2 | semidirect |
| 9. C22×#13083551 | C22 | semidirect |
| 10. #19151785 | C4 | semidirect |
| 18. #19151470 | C22 | semidirect |
| 19. #19151453 | C22 | semidirect |
| 20. C4×C22⋊Dic89 | C22 | semidirect |
| 21. #19151365 | C22 | semidirect |
| 33. #15667980 | C2×C4 | semidirect |
| 45. #15667927 | C2×C4 | semidirect |
| 55. C23×C4×C89 | D4 | semidirect |
| 69. C2×C4⋊C4×C89 | D4 | semidirect |
| 72. C2×C22⋊C4×C89 | D4 | semidirect |
| 75. C2×C42×C89 | D4 | semidirect |
| 80. C23×D89 | C22×C4 | semidirect |
| 92. C22⋊Dic89 | C22×C4 | semidirect |
| 222. C4×H(5,𝔽2) | D89 | semidirect |
| 229. C89 | #21482 | semidirect |
| 260. C23×C4 | C22⋊D89 | semidirect |
| 277. C2×C4⋊C4 | C22⋊D89 | semidirect |
| 288. C2×C22⋊C4 | C22⋊D89 | semidirect |
| 292. C2×C42 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151785 | 2 |
| #26022906 | 2 |
| #26020660 | 2 |
| #26020533 | 2 |
| #26020200 | 2 |
| C4×#15667927 | 2 |
| C4×H(5,𝔽2)×C89 | 2 |
| #21482 | 89 |