Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
2014 conjugacy classes of subgroups; only the 355 normal subgroups are shown.
This group has 2014 conjugacy classes of subgroups — too many to draw. Only its 355 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×#19151443 | C2 | semidirect |
| 3. #26018523 | C2 | semidirect |
| 5. #26018488 | C2 | semidirect |
| 6. C89×#1446 | C2 | semidirect |
| 9. C2×#15668001 | C4 | semidirect |
| 71. C4×Dic89 | C22⋊C4 | semidirect |
| 158. #1446 | D89 | semidirect |
| 161. C89 | #14169 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668001 | 2 |
| C2×#19151443 | 2 |
| #26018523 | 2 |
| #26018492 | 2 |
| #26018488 | 2 |
| C89×#1446 | 2 |
| #14169 | 89 |