Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1138 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 1138 conjugacy classes of subgroups — too many to draw. Only its 119 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. #26018849 | C2 | semidirect |
| 3. #26018696 | C2 | semidirect |
| 4. #26018593 | C2 | semidirect |
| 5. C4×#100×C89 | C2 | semidirect |
| 18. #19151655 | C22 | semidirect |
| 25. C4×M16×C89 | C22 | semidirect |
| 198. D356 | #100 | semidirect |
| 250. C4×#100 | D89 | semidirect |
| 254. C89 | #8367 | semidirect |
| 270. C4×M16 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152244 | 2 |
| #26018849 | 2 |
| #26018696 | 2 |
| #26018593 | 2 |
| C4×#100×C89 | 2 |
| #8367 | 89 |