Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1060 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 1060 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. #26031000 | C2 | semidirect |
| 2. #26023885 | C2 | semidirect |
| 3. #26021089 | C2 | semidirect |
| 4. #26020183 | C2 | semidirect |
| 5. #26018821 | C2 | semidirect |
| 6. #26018098 | C2 | semidirect |
| 7. C2×#447×C89 | C2 | semidirect |
| 35. C22×#10623494 | D4 | semidirect |
| 68. C22×D4×C89 | D4 | semidirect |
| 77. C2×C4⋊C4×C89 | D4 | semidirect |
| 81. C22⋊C8×C89 | D4 | semidirect |
| 105. C22⋊Dic89 | D8 | semidirect |
| 270. C2×#447 | D89 | semidirect |
| 276. C89 | #9946 | semidirect |
| 312. C22×D4 | C22⋊D89 | semidirect |
| 332. C2×C4⋊C4 | C22⋊D89 | semidirect |
| 348. C22⋊C8 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031000 | 2 |
| #26023885 | 2 |
| #26021089 | 2 |
| #26020183 | 2 |
| #26018821 | 2 |
| #26018098 | 2 |
| C2×#447×C89 | 2 |
| #9946 | 89 |