Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
742 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 742 conjugacy classes of subgroups — too many to draw. Only its 89 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. #26023017 | C2 | semidirect |
| 3. #26020170 | C2 | semidirect |
| 4. #26018782 | C2 | semidirect |
| 5. #26018161 | C2 | semidirect |
| 6. #26018105 | C2 | semidirect |
| 7. C89×#1789 | C2 | semidirect |
| 11. #19151737 | C4 | semidirect |
| 12. #19151732 | C4 | semidirect |
| 58. C22⋊#10623494 | C2×C4 | semidirect |
| 71. C22×Q8×C89 | C2×C4 | semidirect |
| 73. C22×D4×C89 | C2×C4 | semidirect |
| 289. #1789 | D89 | semidirect |
| 294. C89 | #9523 | semidirect |
| 324. C22×Q8 | C4×D89 | semidirect |
| 328. C22×D4 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029504 | 2 |
| #26023017 | 2 |
| #26020170 | 2 |
| #26018782 | 2 |
| #26018161 | 2 |
| #26018105 | 2 |
| C89×#1789 | 2 |
| #9523 | 89 |