Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
808 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 808 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. #26029510 | C2 | semidirect |
| 3. #26021238 | C2 | semidirect |
| 4. #26020195 | C2 | semidirect |
| 5. #26018768 | C2 | semidirect |
| 6. #26018157 | C2 | semidirect |
| 7. C89×#3193 | C2 | semidirect |
| 58. C22⋊#10623494 | D4 | semidirect |
| 62. C22×Q8×C89 | D4 | semidirect |
| 67. C2×M16×C89 | D4 | semidirect |
| 78. C2×C4⋊C4×C89 | D4 | semidirect |
| 270. #3193 | D89 | semidirect |
| 277. C89 | #9934 | semidirect |
| 309. C22×Q8 | C22⋊D89 | semidirect |
| 322. C2×M16 | C22⋊D89 | semidirect |
| 335. C2×C4⋊C4 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029510 | 2 |
| #26025977 | 2 |
| #26021238 | 2 |
| #26020195 | 2 |
| #26018768 | 2 |
| #26018157 | 2 |
| C89×#3193 | 2 |
| #9934 | 89 |