Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1162 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 1162 conjugacy classes of subgroups — too many to draw. Only its 147 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 |
|---|---|---|
| 2. C2×#19151410 | C2 | semidirect |
| 3. #26021863 | C2 | semidirect |
| 4. C89×#1810 | C2 | semidirect |
| 11. C2×#15667952 | C22 | semidirect |
| 15. C2×#108×C89 | C22 | semidirect |
| 111. C22×C89 | #361 | semidirect |
| 131. #1810 | D89 | semidirect |
| 132. C89 | #12736 | semidirect |
| 141. C2×#108 | C2×D89 | semidirect |
| 243. C22 | #19151410 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D712 | 2 |
| C2×#19151410 | 2 |
| #26021863 | 2 |
| C89×#1810 | 2 |
| #12736 | 89 |