Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1408 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 1408 conjugacy classes of subgroups — too many to draw. Only its 187 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. #26031005 | C2 | semidirect |
| 3. #26019271 | C2 | semidirect |
| 4. #26019203 | C2 | semidirect |
| 5. #26018819 | C2 | semidirect |
| 6. C2×#19151322 | C2 | semidirect |
| 7. C89×#2626 | C2 | semidirect |
| 17. #19151916 | C22 | semidirect |
| 20. #19151737 | C22 | semidirect |
| 21. C2×C22⋊#10623494 | C22 | semidirect |
| 22. #19151331 | C22 | semidirect |
| 23. #19151322 | C22 | semidirect |
| 24. C2×C22⋊Q8×C89 | C22 | semidirect |
| 26. #399×C89 | C22 | semidirect |
| 28. #393×C89 | C22 | semidirect |
| 30. #380×C89 | C22 | semidirect |
| 62. C22⋊#10623494 | C23 | semidirect |
| 64. C22×Q8×C89 | C23 | semidirect |
| 72. C2×C4⋊C4×C89 | C23 | semidirect |
| 82. #95×C89 | C23 | semidirect |
| 119. C24×C89 | SD16 | semidirect |
| 248. #2626 | D89 | semidirect |
| 253. C89 | #18285 | semidirect |
| 259. C2×C22⋊Q8 | C2×D89 | semidirect |
| 270. #399 | C2×D89 | semidirect |
| 272. #393 | C2×D89 | semidirect |
| 274. #380 | C2×D89 | semidirect |
| 280. C22×Q8 | C22×D89 | semidirect |
| 311. C2×C4⋊C4 | C22×D89 | semidirect |
| 328. #95 | C22×D89 | semidirect |
| 339. C24 | #13083561 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152160 | 2 |
| #26031005 | 2 |
| #26019271 | 2 |
| #26019203 | 2 |
| #26018819 | 2 |
| C2×#19151322 | 2 |
| C89×#2626 | 2 |
| #18285 | 89 |