Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
662 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 81 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. #26030720 | C2 | semidirect |
| 2. #26026104 | C2 | semidirect |
| 3. #26018875 | C2 | semidirect |
| 4. #26018799 | C2 | semidirect |
| 5. #26018695 | C2 | semidirect |
| 6. #26018118 | C2 | semidirect |
| 7. C89×#3109 | C2 | semidirect |
| 55. C4×#10623494 | D4 | semidirect |
| 64. C4⋊Q8×C89 | D4 | semidirect |
| 65. #127×C89 | D4 | semidirect |
| 83. #97×C89 | D4 | semidirect |
| 229. #3109 | D89 | semidirect |
| 235. C89 | #10018 | semidirect |
| 275. C4⋊Q8 | C22⋊D89 | semidirect |
| 276. #127 | C22⋊D89 | semidirect |
| 306. #97 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030720 | 2 |
| #26026104 | 2 |
| #26018875 | 2 |
| #26018799 | 2 |
| #26018695 | 2 |
| #26018118 | 2 |
| C89×#3109 | 2 |
| #10018 | 89 |