Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1026 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 1026 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. #26021050 | C2 | semidirect |
| 3. #26018948 | C2 | semidirect |
| 4. #26018947 | C2 | semidirect |
| 5. #26018862 | C2 | semidirect |
| 6. #26018592 | C2 | semidirect |
| 7. C89×#1530 | C2 | semidirect |
| 20. #19151655 | C22 | semidirect |
| 21. C2×C4⋊#10623494 | C22 | semidirect |
| 30. #432×C89 | C22 | semidirect |
| 31. C2×#97×C89 | C22 | semidirect |
| 248. #1530 | D89 | semidirect |
| 250. C89 | #8456 | semidirect |
| 265. #432 | C2×D89 | semidirect |
| 268. C2×#97 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034014 | 2 |
| #26021050 | 2 |
| #26018948 | 2 |
| #26018947 | 2 |
| #26018862 | 2 |
| #26018592 | 2 |
| C89×#1530 | 2 |
| #8456 | 89 |