Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
324 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 99 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×#19151373 | C2 | semidirect |
| 5. #26020998 | C2 | semidirect |
| 6. #26018349 | C2 | semidirect |
| 7. C89×#1381 | C2 | semidirect |
| 16. #19151403 | C4 | semidirect |
| 17. #19151400 | C4 | semidirect |
| 144. #1381 | D89 | semidirect |
| 145. C89 | #13152 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151404 | 2 |
| #26021960 | 2 |
| C2×#19151373 | 2 |
| #26021138 | 2 |
| #26020998 | 2 |
| #26018349 | 2 |
| C89×#1381 | 2 |
| #13152 | 89 |