Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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. C22×#15667956 | C2 | semidirect |
| 2. C2×#19151873 | C2 | semidirect |
| 3. C2×#19151411 | C2 | semidirect |
| 4. #26021971 | C2 | semidirect |
| 5. C2×#19151382 | C2 | semidirect |
| 6. #26018347 | C2 | semidirect |
| 37. C2×Dic356 | D4 | semidirect |
| 47. C2×#13083549 | D4 | semidirect |
| 49. #15667948 | D4 | semidirect |
| 202. C89 | #13321 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15667956 | 2 |
| C2×#19151873 | 2 |
| C2×#19151411 | 2 |
| #26021971 | 2 |
| C2×#19151382 | 2 |
| #26018347 | 2 |
| C89×#3058 | 2 |
| #13321 | 89 |