Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
818 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 818 conjugacy classes of subgroups — too many to draw. Only its 107 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×#19151386 | C2 | semidirect |
| 3. #26020170 | C2 | semidirect |
| 4. #26018371 | C2 | semidirect |
| 5. C2×#413×C89 | C2 | semidirect |
| 6. C2×#15667980 | C4 | semidirect |
| 8. C22×#13083551 | C4 | semidirect |
| 13. #19151478 | C4 | semidirect |
| 18. #19151461 | C4 | semidirect |
| 71. #100×C89 | D4 | semidirect |
| 267. C2×#413 | D89 | semidirect |
| 272. C89 | #13083 | semidirect |
| 329. #100 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023567 | 2 |
| C2×#19151386 | 2 |
| #26020170 | 2 |
| #26018371 | 2 |
| C2×#413×C89 | 2 |
| #13083 | 89 |