Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
810 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 810 conjugacy classes of subgroups — too many to draw. Only its 115 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. #26021051 | C2 | semidirect |
| 3. #26018841 | C2 | semidirect |
| 4. #26018666 | C2 | semidirect |
| 5. C4×#100×C89 | C2 | semidirect |
| 18. C2×C4⋊#10623494 | C22 | semidirect |
| 21. C2×#15667923 | C22 | semidirect |
| 28. C4×M16×C89 | C22 | semidirect |
| 263. C4×#100 | D89 | semidirect |
| 266. C89 | #8401 | semidirect |
| 284. C4×M16 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033661 | 2 |
| #26021051 | 2 |
| #26018841 | 2 |
| #26018666 | 2 |
| C4×#100×C89 | 2 |
| #8401 | 89 |