Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
510 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 147 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 |
|---|---|---|
| 3. C2×#19151375 | C2 | semidirect |
| 4. #26018332 | C2 | semidirect |
| 5. C89×#1375 | C2 | semidirect |
| 14. #19151377 | C4 | semidirect |
| 35. C2×#13083549 | C2×C4 | semidirect |
| 44. C2×C16×C89 | C2×C4 | semidirect |
| 118. C2×D89 | #347 | semidirect |
| 136. #1375 | D89 | semidirect |
| 137. C89 | #12605 | semidirect |
| 173. C2×C16 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#97×D89 | 2 |
| #26021862 | 2 |
| C2×#19151375 | 2 |
| #26018332 | 2 |
| C89×#1375 | 2 |
| #12605 | 89 |