Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
794 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 105 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. #26031167 | C2 | semidirect |
| 2. #26025198 | C2 | semidirect |
| 3. #26018921 | C2 | semidirect |
| 4. #26018747 | C2 | semidirect |
| 5. #26018643 | C2 | semidirect |
| 6. #26018153 | C2 | semidirect |
| 7. C89×#3036 | C2 | semidirect |
| 47. C4⋊#10623494 | D4 | semidirect |
| 62. C4⋊Q8×C89 | D4 | semidirect |
| 63. #127×C89 | D4 | semidirect |
| 77. C4⋊C8×C89 | D4 | semidirect |
| 119. C2×D4×C89 | D8 | semidirect |
| 242. #3036 | D89 | semidirect |
| 248. C89 | #10238 | semidirect |
| 285. C4⋊Q8 | C22⋊D89 | semidirect |
| 292. #127 | C22⋊D89 | semidirect |
| 312. C4⋊C8 | C22⋊D89 | semidirect |
| 352. C2×D4 | #13083559 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031167 | 2 |
| #26025198 | 2 |
| #26018921 | 2 |
| #26018747 | 2 |
| #26018643 | 2 |
| #26018153 | 2 |
| C89×#3036 | 2 |
| #10238 | 89 |