Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
654 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 654 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 1. #26031251 | C2 | semidirect |
| 3. #26021197 | C2 | semidirect |
| 4. #26018851 | C2 | semidirect |
| 5. #26018695 | C2 | semidirect |
| 6. #26018107 | C2 | semidirect |
| 7. C89×#3110 | C2 | semidirect |
| 52. C4⋊#10623494 | D4 | semidirect |
| 63. C4⋊Q8×C89 | D4 | semidirect |
| 64. C4⋊Q8×C89 | D4 | semidirect |
| 83. #97×C89 | D4 | semidirect |
| 229. #3110 | D89 | semidirect |
| 235. C89 | #10008 | semidirect |
| 270. C4⋊Q8 | C22⋊D89 | semidirect |
| 271. C4⋊Q8 | C22⋊D89 | semidirect |
| 309. #97 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031251 | 2 |
| #26025191 | 2 |
| #26021197 | 2 |
| #26018851 | 2 |
| #26018695 | 2 |
| #26018107 | 2 |
| C89×#3110 | 2 |
| #10008 | 89 |