Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
564 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 564 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. #26028842 | C2 | semidirect |
| 3. #26021969 | C2 | semidirect |
| 4. #26018358 | C2 | semidirect |
| 5. C2×#349×C89 | C2 | semidirect |
| 10. #19151851 | C4 | semidirect |
| 25. C2×D712 | C2×C4 | semidirect |
| 38. #15667946 | D4 | semidirect |
| 42. #15667944 | C2×C4 | semidirect |
| 160. C2×#349 | D89 | semidirect |
| 162. C89 | #12999 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151851 | 2 |
| #26028842 | 2 |
| #26021969 | 2 |
| #26018358 | 2 |
| C2×#349×C89 | 2 |
| #12999 | 89 |