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. #26031054 | C2 | semidirect |
| 3. #26021238 | C2 | semidirect |
| 4. #26020196 | C2 | semidirect |
| 5. #26018769 | C2 | semidirect |
| 6. #26018159 | C2 | semidirect |
| 7. C89×#3007 | C2 | semidirect |
| 37. C2×#13083558 | D4 | semidirect |
| 66. C22×Q8×C89 | D4 | semidirect |
| 80. C2×C4⋊C4×C89 | D4 | semidirect |
| 85. C22⋊C8×C89 | D4 | semidirect |
| 271. #3007 | D89 | semidirect |
| 277. C89 | #9934 | semidirect |
| 309. C22×Q8 | C22⋊D89 | semidirect |
| 335. C2×C4⋊C4 | C22⋊D89 | semidirect |
| 352. C22⋊C8 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031054 | 2 |
| #26025976 | 2 |
| #26021238 | 2 |
| #26020196 | 2 |
| #26018769 | 2 |
| #26018159 | 2 |
| C89×#3007 | 2 |
| #9934 | 89 |