Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
734 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 734 conjugacy classes of subgroups — too many to draw. Only its 101 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. #26030248 | C2 | semidirect |
| 2. #26023531 | C2 | semidirect |
| 3. #26021085 | C2 | semidirect |
| 4. #26018678 | C2 | semidirect |
| 5. #26018677 | C2 | semidirect |
| 6. #26018080 | C2 | semidirect |
| 7. C89×#3100 | C2 | semidirect |
| 58. C4×#10623494 | D4 | semidirect |
| 65. C4⋊Q8×C89 | D4 | semidirect |
| 66. #127×C89 | D4 | semidirect |
| 84. C4×C8×C89 | D4 | semidirect |
| 110. C4×Dic89 | D8 | semidirect |
| 237. #3100 | D89 | semidirect |
| 243. C89 | #10012 | semidirect |
| 278. C4⋊Q8 | C22⋊D89 | semidirect |
| 279. #127 | C22⋊D89 | semidirect |
| 318. C4×C8 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030248 | 2 |
| #26023531 | 2 |
| #26021085 | 2 |
| #26018678 | 2 |
| #26018677 | 2 |
| #26018080 | 2 |
| C89×#3100 | 2 |
| #10012 | 89 |