Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
700 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 700 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. #26023363 | C2 | semidirect |
| 3. C2×#19151394 | C2 | semidirect |
| 4. #26020211 | C2 | semidirect |
| 5. #26018379 | C2 | semidirect |
| 6. #26018378 | C2 | semidirect |
| 7. C89×#1793 | C2 | semidirect |
| 11. #19151771 | C4 | semidirect |
| 59. #15667931 | C2×C4 | semidirect |
| 68. 2−1+4×C89 | C2×C4 | semidirect |
| 269. #1793 | D89 | semidirect |
| 272. C89 | #13057 | semidirect |
| 299. 2−1+4 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151771 | 2 |
| #26023363 | 2 |
| C2×#19151394 | 2 |
| #26020211 | 2 |
| #26018379 | 2 |
| #26018378 | 2 |
| C89×#1793 | 2 |
| #13057 | 89 |