Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
698 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 83 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×#19151322 | C2 | semidirect |
| 3. #26018272 | C2 | semidirect |
| 4. #26018248 | C2 | semidirect |
| 5. C89×#1819 | C2 | semidirect |
| 6. C22×#13083574 | C4 | semidirect |
| 9. #19151510 | C4 | semidirect |
| 11. #19151507 | C4 | semidirect |
| 16. #19151461 | C4 | semidirect |
| 236. #1819 | D89 | semidirect |
| 240. C89 | #11839 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023571 | 2 |
| C2×#19151322 | 2 |
| #26018272 | 2 |
| #26018248 | 2 |
| C89×#1819 | 2 |
| #11839 | 89 |