Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
680 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 680 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 |
|---|---|---|
| 2. C2×#19151395 | C2 | semidirect |
| 3. #26020210 | C2 | semidirect |
| 4. #26018379 | C2 | semidirect |
| 5. C89×#2379 | C2 | semidirect |
| 9. #19151770 | C4 | semidirect |
| 25. #15668060 | C2×C4 | semidirect |
| 43. #15667931 | C2×C4 | semidirect |
| 194. #2379 | D89 | semidirect |
| 198. C89 | #13055 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151770 | 2 |
| C2×#19151395 | 2 |
| #26020210 | 2 |
| #26018379 | 2 |
| C89×#2379 | 2 |
| #13055 | 89 |