Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
576 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 576 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. #26023406 | C2 | semidirect |
| 3. #26018781 | C2 | semidirect |
| 4. #26018767 | C2 | semidirect |
| 5. #26018158 | C2 | semidirect |
| 6. #26018105 | C2 | semidirect |
| 7. C89×#1964 | C2 | semidirect |
| 9. #19151916 | C4 | semidirect |
| 12. #19151732 | C4 | semidirect |
| 55. C22⋊#10623494 | C2×C4 | semidirect |
| 62. C22×D4×C89 | C2×C4 | semidirect |
| 69. C2×C4⋊C4×C89 | C2×C4 | semidirect |
| 251. #1964 | D89 | semidirect |
| 256. C89 | #9343 | semidirect |
| 283. C22×D4 | C4×D89 | semidirect |
| 300. C2×C4⋊C4 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031049 | 2 |
| #26023406 | 2 |
| #26018781 | 2 |
| #26018767 | 2 |
| #26018158 | 2 |
| #26018105 | 2 |
| C89×#1964 | 2 |
| #9343 | 89 |