Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
850 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 850 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. #26031049 | C2 | semidirect |
| 2. #26025976 | C2 | semidirect |
| 3. #26021089 | C2 | semidirect |
| 4. #26020196 | C2 | semidirect |
| 5. #26018769 | C2 | semidirect |
| 6. #26018159 | C2 | semidirect |
| 7. C89×#3006 | C2 | semidirect |
| 37. C2×#13083558 | D4 | semidirect |
| 70. C22×D4×C89 | D4 | semidirect |
| 81. C2×C4⋊C4×C89 | D4 | semidirect |
| 86. C22⋊C8×C89 | D4 | semidirect |
| 283. #3006 | D89 | semidirect |
| 289. C89 | #9930 | semidirect |
| 327. C22×D4 | C22⋊D89 | semidirect |
| 347. C2×C4⋊C4 | C22⋊D89 | semidirect |
| 365. C22⋊C8 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031049 | 2 |
| #26025976 | 2 |
| #26021089 | 2 |
| #26020196 | 2 |
| #26018769 | 2 |
| #26018159 | 2 |
| C89×#3006 | 2 |
| #9930 | 89 |