Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1652 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 1652 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×#19151737 | C2 | semidirect |
| 3. #26019203 | C2 | direct (N × H) |
| 4. C2×#19151331 | C2 | semidirect |
| 5. C2×#19151322 | C2 | semidirect |
| 6. C2×#393×C89 | C2 | semidirect |
| 17. #19151737 | C22 | semidirect |
| 19. C2×C22⋊#10623494 | C22 | semidirect |
| 20. #19151331 | C22 | semidirect |
| 21. #19151322 | C22 | semidirect |
| 22. C23×Q8×C89 | C22 | semidirect |
| 26. #393×C89 | C22 | semidirect |
| 28. C2×#95×C89 | C22 | semidirect |
| 58. C22⋊#10623494 | C23 | semidirect |
| 64. C22×Q8×C89 | C23 | semidirect |
| 77. #95×C89 | C23 | semidirect |
| 114. C24×C89 | SD16 | semidirect |
| 162. C23×C89 | C2×SD16 | semidirect |
| 242. C2×C89 | #1601 | semidirect |
| 249. C2×#393 | D89 | semidirect |
| 253. C89 | C2×#1601 | semidirect |
| 254. C23×Q8 | C2×D89 | semidirect |
| 271. #393 | C2×D89 | semidirect |
| 273. C2×#95 | C2×D89 | semidirect |
| 282. C22×Q8 | C22×D89 | semidirect |
| 324. #95 | C22×D89 | semidirect |
| 335. C24 | #13083561 | semidirect |
| 417. C23 | C2×#13083561 | semidirect |
| 489. C2 | #26019203 | 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×#19151737 | 2 |
| #26019203 | 2 |
| C2×#19151331 | 2 |
| C2×#19151322 | 2 |
| C2×#393×C89 | 2 |
| C2×#1601 | 89 |