Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
334 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 4. #26021037 | C2 | semidirect |
| 5. #26018361 | C2 | semidirect |
| 6. #26018346 | C2 | semidirect |
| 7. C89×#2108 | C2 | semidirect |
| 15. #19151412 | C4 | semidirect |
| 147. #2108 | D89 | semidirect |
| 152. C89 | #13144 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151412 | 2 |
| C2×#19151400 | 2 |
| #26021162 | 2 |
| #26021037 | 2 |
| #26018361 | 2 |
| #26018346 | 2 |
| C89×#2108 | 2 |
| #13144 | 89 |