Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
516 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 127 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. #26021987 | C2 | semidirect |
| 3. C2×#19151380 | C2 | semidirect |
| 4. #26018353 | C2 | semidirect |
| 5. C89×#2911 | C2 | semidirect |
| 9. #19151856 | C4 | semidirect |
| 10. #19151851 | C4 | semidirect |
| 24. C2×Dic356 | C2×C4 | semidirect |
| 26. C2×D712 | C2×C4 | semidirect |
| 37. #15667944 | C2×C4 | semidirect |
| 57. #106×C89 | D4 | semidirect |
| 163. #2911 | D89 | semidirect |
| 167. C89 | #13008 | semidirect |
| 217. #106 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029861 | 2 |
| #26021987 | 2 |
| C2×#19151380 | 2 |
| #26018353 | 2 |
| C89×#2911 | 2 |
| #13008 | 89 |