Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
338 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 338 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. C2×#19151421 | C2 | semidirect |
| 5. #26020149 | C2 | semidirect |
| 6. #26018361 | C2 | semidirect |
| 7. C89×#1375 | C2 | semidirect |
| 17. #19151403 | C4 | semidirect |
| 18. #19151400 | C4 | semidirect |
| 155. #1375 | D89 | semidirect |
| 156. C89 | #13143 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151421 | 2 |
| C2×#19151409 | 2 |
| #26021965 | 2 |
| #26021145 | 2 |
| #26020149 | 2 |
| #26018361 | 2 |
| C89×#1375 | 2 |
| #13143 | 89 |