Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
420 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 420 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. #26020298 | C2 | semidirect |
| 4. #26018372 | C2 | semidirect |
| 5. C89×#1812 | C2 | semidirect |
| 6. C2×#15668018 | C4 | semidirect |
| 13. #19151621 | C4 | semidirect |
| 15. #19151566 | C4 | semidirect |
| 17. C2×#15667922 | C4 | semidirect |
| 189. #1812 | D89 | semidirect |
| 191. C89 | #12808 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028968 | 2 |
| #26021915 | 2 |
| #26020298 | 2 |
| #26018372 | 2 |
| C89×#1812 | 2 |
| #12808 | 89 |