Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
2040 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 2040 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 |
|---|---|---|
| 1. C2×#19152160 | C2 | semidirect |
| 2. C2×#19151732 | C2 | semidirect |
| 3. #26019169 | C2 | direct (N × H) |
| 4. C2×#19151331 | C2 | semidirect |
| 5. C2×#19151322 | C2 | semidirect |
| 6. C2×#392×C89 | C2 | semidirect |
| 11. #19152160 | C22 | semidirect |
| 17. #19151732 | C22 | semidirect |
| 19. C2×C22⋊#10623494 | C22 | semidirect |
| 20. #19151331 | C22 | semidirect |
| 21. #19151322 | C22 | semidirect |
| 23. C23×D4×C89 | C22 | semidirect |
| 27. #392×C89 | C22 | semidirect |
| 28. C2×#95×C89 | C22 | semidirect |
| 31. C22×D356 | D4 | semidirect |
| 48. #15667986 | D4 | semidirect |
| 53. C2×C4⋊Dic89 | D4 | semidirect |
| 58. C22⋊#10623494 | C23 | semidirect |
| 69. C22×D4×C89 | C23 | semidirect |
| 80. #95×C89 | C23 | semidirect |
| 90. C2×D356 | C2×D4 | semidirect |
| 108. C4⋊Dic89 | C2×D4 | semidirect |
| 126. C24×C89 | D8 | semidirect |
| 190. C23×C89 | C2×D8 | semidirect |
| 275. C2×C89 | #1595 | semidirect |
| 282. C2×#392 | D89 | semidirect |
| 286. C89 | C2×#1595 | semidirect |
| 289. C23×D4 | C2×D89 | semidirect |
| 305. #392 | C2×D89 | semidirect |
| 306. C2×#95 | C2×D89 | semidirect |
| 328. C22×D4 | C22×D89 | semidirect |
| 360. #95 | C22×D89 | semidirect |
| 380. C24 | #13083559 | semidirect |
| 478. C23 | C2×#13083559 | semidirect |
| 555. C2 | #26019169 | 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×#19151732 | 2 |
| #26019169 | 2 |
| C2×#19151331 | 2 |
| C2×#19151322 | 2 |
| C2×#392×C89 | 2 |
| C2×#1595 | 89 |